properties of exponents - numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43...

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Page 1: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 2: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

13)

32 ⋅

33

14)

(−4)2 ⋅

(−4)4

15)

23 ⋅

24

16)

4 ⋅

43

17)

(−3)3 ⋅

(−3)3 18)

(−3)0 ⋅

(−3)4

19)

20 ⋅

24

20)

−2 ⋅

(−2)4

21)

4 ⋅

44

22)

(−2)3 ⋅

(−2)2

23)

−2 ⋅

(−2)0 24)

(−2)4 ⋅

(−2)2

25)

−4 ⋅

(−4)2 26)

3 ⋅

34

-2-

Page 3: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

27)

3 ⋅

34

28)

−3 ⋅

(−3)3

29)

(−2)3 ⋅

(−2)3 30)

40 ⋅

44

31)

16 ⋅

(−4)2 32)

(−4)3 ⋅

(−4)2 ⋅

(−4)0

33)

2 ⋅

22 ⋅

23

34)

3 ⋅

34 ⋅

32

35)

2 ⋅

24

36)

4 ⋅

44 ⋅

44

37)

34 ⋅

30

38)

43 ⋅

40

39)

30 ⋅

32

40)

44 ⋅

42

-3-

Page 4: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

41)

−2 ⋅

(−2)3 42)

23 ⋅

22

43)

34 ⋅

32

44)

(−3)0 ⋅

(−3)3

45)

(−3)3 ⋅

(−3)2 46)

24 ⋅

24

47)

−2 ⋅

(−2)2 48)

−3 ⋅

(−3)0

49)

−2 ⋅

(−2)2 50)

−4 ⋅

(−4)0

51)

2 ⋅

20 ⋅

23

52)

(−4)0 ⋅

(−4)3

53)

16 ⋅

(−4)3 54)

20 ⋅

20

-4-

Page 5: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

55)

(−2)3 ⋅

(−2)3 ⋅

(−2)2 56)

(−4)4 ⋅

(−4)3

57)

(−3)4 ⋅

(−3)4 58)

20 ⋅

23

59)

(−3)2 ⋅

(−3)0 60)

−3 ⋅

(−3)0

61)

4 ⋅

40

62)

2 ⋅

22

63)

42 ⋅

42

64)

(−2)0 ⋅

(−2)3

65)

(−2)2 ⋅

(−2)3 66)

33 ⋅

34

67)

(−3)2 ⋅

(−3)3 68)

(−3)3 ⋅

(−3)4

-5-

Page 6: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

69)

34 ⋅

33

70)

16 ⋅

43

71)

2 ⋅

24 ⋅

20

72)

9 ⋅

33

73)

(−4)4 ⋅

(−4)3 ⋅

(−4)3 74)

(−2)3 ⋅

(−2)4 ⋅

(−2)4

75)

−2 ⋅

(−2)3 76)

−2 ⋅

(−2)4

77)

−4 ⋅

(−4)0 78)

(−3)2 ⋅

(−3)4

79)

(−3)3 ⋅

(−3)0 80)

33 ⋅

32

81)

9 ⋅

(−3)3 82)

(−3)2 ⋅

(−3)2 ⋅

(−3)3

-6-

Page 7: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

83)

4 ⋅

(−2)3 84)

4 ⋅

40 ⋅

44

85)

3 ⋅

33 ⋅

32

86)

−4 ⋅

(−4)4

87)

−4 ⋅

(−4)2 88)

2 ⋅

22

89)

22 ⋅

23

90)

(−4)2 ⋅

(−4)3

91)

43 ⋅

42

92)

(−3)4 ⋅

(−3)3

93)

33 ⋅

30

94)

44 ⋅

44

95)

32 ⋅

33 ⋅

34

96)

−4 ⋅

(−4)4 ⋅

(−4)3

-7-

Page 8: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

97)

(−4)4 ⋅

(−4)4 ⋅

(−4)2 98)

−3 ⋅

(−3)2 ⋅

(−3)2

99)

(−2)2 ⋅

(−2)2 100)

32 ⋅

32

101)

(−4)3 ⋅

(−4)7 ⋅

(−4)−8 102)

6 ⋅

65 ⋅

68

103)

−4 ⋅

(−4)2 ⋅

(−4)−8 104)

(−5)6 ⋅

(−5)−7 ⋅

(−5)7

105)

33 ⋅

32

106)

(−2)2 ⋅

(−2)4

107)

(−3)−6 ⋅

(−3)−5 108)

−4 ⋅

(−4)−1

109)

(−7)−4 ⋅

(−7)−5 110)

76 ⋅

7−6

-8-

Page 9: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

111)

(−2)0 ⋅

(−2)7 112)

6 ⋅

62

113)

43 ⋅

45

114)

(−7)−5 ⋅

(−7)8

115)

(−7)5 ⋅

(−7)7 116)

4 ⋅

47

117)

47 ⋅

46

118)

4 ⋅

40

119)

4 ⋅

4−3

120)

(−3)4 ⋅

(−3)−4

121)

(−2)6 ⋅

(−2)4 122)

36 ⋅

37

123)

(−6)0 ⋅

(−6)3 124)

−7 ⋅

(−7)3

-9-

Page 10: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

125)

(−3)2 ⋅

(−3)5 126)

(−7)−4 ⋅

(−7)0

127)

55 ⋅

53

128)

80 ⋅

83

129)

(−3)7 ⋅

(−3)−8 130)

7−7

7−1

131)

−4 ⋅

(−4)6 ⋅

(−4)2 132)

(−3)−8 ⋅

(−3)5 ⋅

(−3)−1

133)

−8 ⋅

(−8)−1 ⋅

(−8)−1 134)

(−7)0 ⋅

(−7)2 ⋅

(−7)−1

135)

(−2)0 ⋅

(−2)5 136)

(−3)3 ⋅

(−3)4

137)

(−7)−6 ⋅

(−7)2 138)

−4 ⋅

(−4)7

-10-

Page 11: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

139)

4−3

4−6

140)

6−3

62

141)

5−2

5−6

142)

−6 ⋅

(−6)3

143)

6−7

68

144)

2−4

2−6

145)

(−7)−4 ⋅

(−7)8 146)

7−2

77

147)

24 ⋅

27

148)

4−1

47

149)

(−6)4 ⋅

(−6)−3 150)

(−7)0 ⋅

(−7)−4

151)

47 ⋅

44

152)

78 ⋅

74

-11-

Page 12: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

153)

74 ⋅

75

154)

30 ⋅

3−6

155)

54 ⋅

50

156)

(−6)7 ⋅

(−6)−8

157)

4−8

42

158)

8 ⋅

80

159)

−4 ⋅

(−4)4 ⋅

(−4)−2 160)

−6 ⋅

(−6)0 ⋅

(−6)6

161)

(−7)0 ⋅

(−7)4 ⋅

(−7)5 162)

8−6

80 ⋅

80

163)

57 ⋅

50

164)

67 ⋅

68 ⋅

65

165)

−3 ⋅

(−3)−2 166)

7−7

7−4

-12-

Page 13: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

167)

40 ⋅

4−5

168)

(−6)6 ⋅

(−6)7

169)

4 ⋅

42

170)

8 ⋅

82

171)

4 ⋅

46

172)

(−5)−3 ⋅

(−5)8

173)

(−8)−2 ⋅

(−8)7 174)

(−2)−1 ⋅

(−2)7

175)

(−3)5 ⋅

(−3)−2 176)

56 ⋅

54

177)

4 ⋅

46

178)

83 ⋅

8−3

179)

(−6)2 ⋅

(−6)−2 180)

(−8)0 ⋅

(−8)3

-13-

Page 14: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

181)

(−2)7 ⋅

(−2)4 182)

53 ⋅

55

183)

83 ⋅

88

184)

76 ⋅

7−7

185)

2 ⋅

2−7

186)

47 ⋅

4−8

187)

6 ⋅

64

188)

(−8)6 ⋅

(−8)6 ⋅

(−8)5

189)

(−7)5 ⋅

(−7)0 190)

20 ⋅

2−4

20

191)

(−8)2 ⋅

(−8)8 ⋅

(−8)0 192)

(−5)0 ⋅

(−5)4

193)

64 ⋅

62 ⋅

65

194)

−5 ⋅

(−5)5

-14-

Page 15: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

195)

(−6)−7 ⋅

(−6)0 196)

(−7)0 ⋅

(−7)3

197)

74 ⋅

72

198)

4−5

40

199)

(−2)3 ⋅

(−2)7 200)

22 ⋅

28

201)

100 ⋅

108

202)

59 ⋅

54

203)

7−5

77

204)

8−10

810

205)

107 ⋅

107

206)

39 ⋅

34

207)

2−6

2−3

208)

5 ⋅

56

-15-

Page 16: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

209)

8−4

89

210)

45 ⋅

4−10

211)

6 ⋅

65

212)

96 ⋅

94

213)

6 ⋅

65

214)

64 ⋅

67

215)

53 ⋅

5−2

216)

5−1

58

217)

83 ⋅

8−3

218)

2−6

210

28

219)

25 ⋅

23 ⋅

28

220)

84 ⋅

80 ⋅

80

221)

27 ⋅

2−5

20

222)

210

22

-16-

Page 17: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

223)

4 ⋅

4−9

224)

60 ⋅

64

225)

6−1

60

226)

3−7

39

227)

10 ⋅

1010

228)

68 ⋅

69

229)

97 ⋅

9−2

230)

7−10

72

231)

4−6

410

232)

7−1

7−5

233)

58 ⋅

50

234)

55 ⋅

55

235)

10−5

105

236)

9 ⋅

90

-17-

Page 18: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

237)

34 ⋅

310

238)

5−3

5−10

239)

43 ⋅

4−1

240)

75 ⋅

79

241)

92 ⋅

93

242)

2−7

210

243)

5−2

56

244)

10 ⋅

10−7

245)

68 ⋅

62

246)

33 ⋅

35

247)

8−6

8−4

248)

4 ⋅

43 ⋅

4−3

249)

28 ⋅

2−4

20

250)

76 ⋅

7−10

70

-18-

Page 19: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

251)

7 ⋅

70 ⋅

72

252)

96 ⋅

93 ⋅

99

253)

10−8

108

254)

67 ⋅

67

255)

310

3−3

256)

47 ⋅

42

257)

8−2

85

258)

66 ⋅

66

259)

910

90

260)

70 ⋅

70

261)

9−6

9−9

262)

33 ⋅

3−10

263)

30 ⋅

3−2

264)

58 ⋅

55

-19-

Page 20: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

265)

79 ⋅

78

266)

9−7

90

267)

9 ⋅

96

268)

62 ⋅

68

269)

90 ⋅

93

270)

710

72

271)

82 ⋅

89

272)

410

45

273)

39 ⋅

3−9

274)

8−2

8−8

275)

63 ⋅

69

276)

80 ⋅

8−1

277)

88 ⋅

89

278)

57 ⋅

50 ⋅

57

-20-

Page 21: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

279)

4−4

4−2

280)

94 ⋅

96 ⋅

90

281)

7−1

74 ⋅

70

282)

85 ⋅

83

283)

100 ⋅

103

284)

94 ⋅

99

285)

6−1

63 ⋅

6−10

286)

210

2−5

287)

74 ⋅

710

288)

40 ⋅

42

289)

2−5

210

290)

5−1

57

291)

90 ⋅

97

292)

83 ⋅

83

-21-

Page 22: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

293)

64 ⋅

60

294)

32 ⋅

32

295)

103 ⋅

100

296)

9−3

9−7

297)

710

7−10

298)

30 ⋅

33

299)

5 ⋅

510

300)

5−8

50

301)

62 ⋅

64

302)

3−2

38

303)

96 ⋅

98

304)

87 ⋅

8−3

305)

5−1

510

306)

9−9

9−6

-22-

Page 23: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

307)

4−5

43

308)

4 ⋅

40

309)

3 ⋅

3−9

39

310)

29 ⋅

2−8

20

311)

2 ⋅

2−7

2−6

312)

4−5

4−3

40

313)

39 ⋅

3−6

32

314)

62 ⋅

69

315)

910

9−2

316)

2 ⋅

23

317)

20 ⋅

26

318)

1010

103

319)

5−5

5−5

320)

8−1

85

-23-

Page 24: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

321)

38 ⋅

3−8

322)

9−4

910

323)

6−9

62

324)

8−7

85

325)

77 ⋅

79

326)

100 ⋅

10−1

327)

49 ⋅

44

328)

3−6

36

329)

3−4

30

330)

66 ⋅

6−4

331)

60 ⋅

60

332)

92 ⋅

96

333)

25 ⋅

20

334)

44 ⋅

4−7

-24-

Page 25: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

335)

10−1

105

336)

23 ⋅

2−10

337)

20 ⋅

27

338)

6−6

60

339)

72 ⋅

70 ⋅

70

340)

510

5−3

50

341)

85 ⋅

85

342)

9−6

97 ⋅

92

343)

810

8−1

89

344)

5−6

510

345)

77 ⋅

76 ⋅

78

346)

89 ⋅

84

347)

10 ⋅

103

348)

37 ⋅

3−10

-25-

Page 26: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 27: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

363)

72 ⋅

7−1

364)

3−1

3−2

365)

70 ⋅

7−4

366)

67 ⋅

60

367)

9−4

90

368)

3−8

3−5

369)

610

63

370)

20 ⋅

2−8

371)

6 ⋅

63 ⋅

6−9

372)

10 ⋅

109 ⋅

100

373)

7 ⋅

76 ⋅

74

374)

6−2

64 ⋅

64

375)

47 ⋅

410

376)

33 ⋅

3−1

-27-

Page 28: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

377)

67 ⋅

64

378)

7−4

74

379)

610

6−7

380)

45 ⋅

4−4

381)

9−9

97

382)

25 ⋅

23

383)

63 ⋅

6−10

384)

3 ⋅

39

385)

70 ⋅

77

386)

49 ⋅

4−8

387)

46 ⋅

45

388)

52 ⋅

510

389)

7 ⋅

7−3

390)

9−6

98

-28-

Page 29: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

391)

32 ⋅

3−6

392)

2 ⋅

2−3

393)

8−1

87

394)

39 ⋅

34

395)

4 ⋅

4−8

396)

104 ⋅

104

397)

70 ⋅

710

398)

6−4

6−9

399)

25 ⋅

25

400)

210

20

401)

(−2)2 ⋅

(

(−2)0)3

402)

(

(−2)0)−3

(−2)2

-29-

Page 30: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

403)

−2 ⋅

(

(−2)−1)4

404)

(

24)−3 ⋅

22

405)

(

22)−2 ⋅

23 ⋅

2−2 406)

(−2)3 ⋅

(−2)−2 ⋅

(−2)−4

407)

23 ⋅

2−3

(

2−2)0 408)

(

2−3)0 ⋅

(

2−4)−1

409)

(

2 ⋅

(

20)0)

2

410)

(

2−4

24)4

411)

24 ⋅

2−4

412)

(−2)3 ⋅

(−2)4

413)

(−2)2 ⋅

(

(−2)2)4

414)

−2 ⋅

(−2)−2

-30-

Page 31: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

415)

(

22)−4 ⋅

23

416)

(−2)4 ⋅

(

(−2)3)−4

417)

(−2)0 ⋅

(

(−2)4)0

418)

(

22)−1 ⋅

(

20)2

419)

(−2)0 ⋅

(−2)2 420)

(

(−2)2 ⋅

(−2)3)2

421)

(

(−2)4 ⋅

(−2)−3)−3

422)

(

2−1)−1 ⋅

(

23)2

423)

(

20)3 ⋅

2−4

424)

(

(−2)4)0

(−2)3

425)

2−1

(

2−3)0 426)

22 ⋅

24

-31-

Page 32: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

427)

(

23)3 ⋅

2−2

428)

23 ⋅

(

23)−3

429)

(

(−2)3)2

(−2)0 430)

42

431)

(

2−2)4 ⋅

24

432)

(

2 ⋅

24)−4

433)

(

23)−4 ⋅

2−1

434)

(

(−2)3)2

(

(−2)−1)2

(−2)0

435)

(

(−2)−1)2

(−2)3 ⋅

(−2)4 436)

2 ⋅

(

24)2

437)

(

22 ⋅

2−3)−3 ⋅

2−3

438)

2 ⋅

(

24)−3

-32-

Page 33: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

439)

(

24)−1 ⋅

20 440)

(−2)0 ⋅

(−2)−1

441)

(

20 ⋅

(

24)4)

4

442)

(

−2 ⋅

(−2)−1)4

443)

2 ⋅

(

2−2)−4 444)

(

(−2)−4)−2

(

(−2)−1)2

445)

(−2)3 ⋅

(

(−2)3)0

446)

(−2)−3 ⋅

(−2)−2

447)

(

(−2)−3)−1

(

(−2)0)3

448)

(

2−1)4 ⋅

2−4

449)

(−2)4 ⋅

(

(−2)2)2

450)

(

(−2)3 ⋅

(−2)4)3

-33-

Page 34: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

451)

(

(−2)2)−2

(−2)0 452)

(−2)−3 ⋅

(

(−2)0)−1

453)

(

(

(−2)−4)3

(−2)3)2

454)

23 ⋅

22

455)

(

(−2)−4)2

(

(−2)−1)3

456)

(

20 ⋅

20)4

457)

2 ⋅

(

22)−2 458)

(

23)4 ⋅

2−3

459)

20 ⋅

(

24)4 460)

(

23)0 ⋅

23

461)

(

2−1)−4 ⋅

20

462)

(

(−2)−3 ⋅

(−2)4)−3

-34-

Page 35: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

463)

(−2)2 ⋅

(−2)4 ⋅

(

(−2)−2)0

464)

(

2 ⋅

2−2)3

465)

2 ⋅

(

22)−3 ⋅

23

466)

(

(−2)4 ⋅

(

(−2)3)3)

2

467)

(

(−2)4)3

(−2)−4 ⋅

(−2)2 468)

(−2)3 ⋅

(

(−2)2)−3

469)

(−2)2 ⋅

(

(−2)−4)−4

470)

(

22)−1 ⋅

2−1

471)

2−1

23

472)

(

(−2)3)4

(−2)3

473)

(

(−2)4)−1

(−2)−1 474)

(

−2 ⋅

(−2)2)3

-35-

Page 36: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

475)

(

(−2)4)2

(

(−2)−4)4

476)

22 ⋅

(

2−2)−2

477)

(

−2 ⋅

(−2)2)3

478)

(

23 ⋅

22)−2

479)

2−4

(

24)2 480)

2−1

(

22)2

481)

−2 ⋅

(

(−2)−2)−2

482)

24 ⋅

(

23)3

483)

(

24)−1 ⋅

24

484)

24 ⋅

(

2−3)3

485)

(

(−2)2)−3

(

(−2)4)3

486)

(

2−1)−3 ⋅

2−3

-36-

Page 37: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

487)

(

2 ⋅

24)−1 488)

(

(−2)2 ⋅

(−2)−2)2

489)

23 ⋅

(

22)3 490)

(

24)−1 ⋅

23

491)

2 ⋅

2−4

492)

2 ⋅

(

24)0

493)

(

24)−4 ⋅

2−4

2−1 494)

2 ⋅

22 ⋅

2−3

495)

4 ⋅

(

23)2 496)

(

(−2)−2)2

(−2)3 ⋅

(−2)2

497)

(

2−2)4 ⋅

22

498)

(

20 ⋅

22)0

-37-

Page 38: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

499)

(

2−1

23)−3 500)

(−2)−1 ⋅

(−2)0

501)

(

2−2)−1 ⋅

23

502)

(

2−1)3 ⋅

2−4

503)

24 ⋅

(

2−3)3 504)

22 ⋅

(

22)−4

505)

(

20)4 ⋅

2−2

506)

(

20)−2 ⋅

(

2−4)3

507)

20 ⋅

(

23)2 508)

2 ⋅

(

20)4

509)

(

24 ⋅

2−3)2 510)

(

2 ⋅

2−4)−2

-38-

Page 39: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

511)

22 ⋅

(

20)2 512)

(

2−1)2 ⋅

(

22)3

513)

22 ⋅

(

2−4)−4 514)

(

22)4 ⋅

(

2−4)0

515)

23 ⋅

23

516)

20 ⋅

(

2−1)0

517)

2−4

(

22)−4 518)

(

22)−2 ⋅

2−2

519)

(

24)3 ⋅

(

22)2 520)

(

2−4

24)0

521)

22 ⋅

(

22)2 522)

(

22)4 ⋅

24

-39-

Page 40: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

523)

(

2−4

20)0 524)

(

2−3)3 ⋅

2−3

24

525)

(

23)−1 ⋅

23 ⋅

20

526)

(

2−1)3 ⋅

2−3

2−2

527)

(

24)2 ⋅

24

528)

24 ⋅

(

24)2

529)

(

20)4 ⋅

2−1

530)

(

22)4 ⋅

23

531)

(

22 ⋅

2−2)−2 532)

(

2 ⋅

22)2

533)

(

24)3 ⋅

20

534)

2 ⋅

(

24)0

-40-

Page 41: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 42: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

547)

20 ⋅

(

22)0 548)

(

23 ⋅

(

2−4)−1)

−4

549)

(

22 ⋅

23)4 550)

(

22)3 ⋅

2−3

551)

(

24)0 ⋅

(

22)0 552)

(

(

23)4 ⋅

2−4)

4

553)

22 ⋅

23

554)

(

2 ⋅

23)−1

555)

2 ⋅

(

22)−1 ⋅

23

556)

(

22 ⋅

2−3)−3 ⋅

23

557)

2−1

(

2−3)2 ⋅

24

558)

(

2 ⋅

(

23)−2)

0

-42-

Page 43: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 44: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

571)

2−3

(

22)2 572)

(

2−1)3 ⋅

20

573)

2−3

24

574)

22 ⋅

(

24)−4

575)

(

2−4

2−4)0 576)

(

24 ⋅

22)3

577)

(

24 ⋅

20)4 578)

(

(

20)−1 ⋅

24)

2

579)

(

2−1)−4 ⋅

20

580)

2−2

(

2−2)3

581)

24 ⋅

(

22)4 582)

22 ⋅

(

2−1)−4 ⋅

2−3

-44-

Page 45: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

583)

(

2−1

2−2)−2 ⋅

(

23)4 584)

(

2−4)2 ⋅

2−4

585)

20 ⋅

(

2−3)0 586)

(

24)3 ⋅

2−3

587)

(

2 ⋅

(

23)0)

−1

588)

(

2−1

24)−2

589)

(

2 ⋅

2−1)0 590)

23 ⋅

(

20)3

591)

(

2−2)4 ⋅

20

592)

2 ⋅

(

24)−1

593)

2−2

23

594)

(

24)−4 ⋅

(

22)3

-45-

Page 46: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

595)

2−1

2−1

596)

(

20)4 ⋅

22

597)

(

2−2

23)3 598)

(

2−1

23)2

599)

20 ⋅

(

2−1)−1 600)

(

20 ⋅

2−3)−3

601)

20 ⋅

(

2−3)−3

2

602)

2−3

(

24)−3 ⋅

24

603)

(

24)2 ⋅

24

2−3

604)

24

20 ⋅

(

22)4

605)

(

(−2)−3)−2

(−2)3

−2

606)

20

2−3

(

23)3

-46-

Page 47: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

607)

22

2 ⋅

(

2−2)4

608)

(

2−4

2−1

24 )

0

609)

(

24

2 ⋅

2−4)

0

610)

(−2)4 ⋅

(−2)0

(

(−2)2)3

611)

2 ⋅

2−2

22

(

22)−4

612)

(

22 ⋅

22

24 )

4

613)

23

22 ⋅

(

20 ⋅

2−2)4

614)

(−2)4 ⋅

(−2)−1

(−2)0

615)

(

(−2)−2)−2

(−2)−3 ⋅

(−2)2 ⋅

(−2)−1616)

(

(−2)−4)3

(−2)−1 ⋅

(−2)−2

-47-

Page 48: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

617)

(

20 ⋅

2−2

2)−1

618)

2−4

(

2−1)−3

(

2−1)4

619)

(−2)0

(−2)−2 ⋅

(−2)2620)

(

(−2)4 ⋅

(−2)−3

−2)2

621)

22 ⋅

(

22)−3

2622)

(

(−2)4 ⋅

(−2)4

(

(−2)−4)4 )

0

623)

(

(−2)−2

(−2)4 ⋅

(−2)3 )3

624)

(

(

2−3)−1 ⋅

22

2−1 )

2

625)

(−2)2 ⋅

(−2)−4

(−2)4626)

(−2)2

(

(−2)2 ⋅

(−2)−2)−1

-48-

Page 49: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

627)

2 ⋅

22

(

2−3)4

628)

(

(−2)−4 ⋅

(−2)4)2

(−2)4

629)

(−2)−2

−2 ⋅

(−2)−2630)

(

22 ⋅

20

2−4 )

0

631)

(

(−2)−4

(

(−2)−4 ⋅

(−2)4)4 )

0

632)

(−2)4 ⋅

(−2)2

(−2)−3

633)

(−2)−3

(

(−2)4)−3

(−2)0634)

(

(−2)−4

(

(

(−2)−4)3

(−2)3)4 )

2

635)

20

22 ⋅

23

636)

(

24)−4 ⋅

2−2

20

-49-

Page 50: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

637)

(

2−3

(

2−4)2

(

2−3)4 )

3

638)

2 ⋅

(−2)3

(−2)2

639)

(

24)3

2−1

2−3

640)

22

22 ⋅

(

2−3)3

641)

(

2 ⋅

22

24 )

−1

642)

20 ⋅

(

22)2

2−2

24

643)

(

(−2)−3 ⋅

(−2)−3

−2)2

644)

(−2)4

(−2)2 ⋅

(−2)4 ⋅

(−2)2

645)

(

(

(−2)−4)3

(−2)0 ⋅

(

(−2)−2)−3

(−2)2)−2

646)

(

(−2)−4)−3

(−2)4 ⋅

(−2)0

-50-

Page 51: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

647)

(

(−2)0

(−2)−4 ⋅

(−2)4 )0

648)

2−1

23

(

24)−2

649)

23

20 ⋅

2−2

650)

(

(−2)3

(−2)3 ⋅

(−2)−1 )3

651)

(

2−4)3

2−3

2−4

652)

(−2)3 ⋅

(−2)−4

(

(−2)3)3

653)

(−2)3 ⋅

(−2)−4

(

(−2)−2)3

654)

(

(−2)−4

(−2)−3 ⋅

(−2)4 )−3

655)

2−1

(

20)2 ⋅

22

656)

(

24 ⋅

2−1)4

20

-51-

Page 52: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

657)

(

2−4

2−3)3

(

24)−1

658)

(

(−2)−1

(−2)−1 ⋅

(−2)−2 )3

659)

(

2

(

24)4 ⋅

(

20)4)

4

660)

(

−2 ⋅

(−2)4)0

(−2)4

661)

(−2)2

(−2)3 ⋅

(

(−2)−3)3

662)

(

(−2)0)−1

(−2)−2 ⋅

(−2)4

663)

(

24 ⋅

2−4

23 )

−2

664)

(−2)3 ⋅

(−2)−4

(

(−2)2)4

665)

2 ⋅

(−2)−3

(

(−2)3)0

666)

(

2−4

23

23 )

4

-52-

Page 53: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

667)

(

(−2)2)−1

(−2)2

(−2)2668)

(

2−1)−1

22 ⋅

24

669)

(

(

22)3 ⋅

22

2)−2

670)

(

(−2)0)−2

(−2)3 ⋅

(−2)3

671)

23

2−1

2−1

672)

(

22)3

2−3

24 ⋅

2−3

673)

(−2)−3

(

(−2)−1)2

(

(−2)3)4

674)

(

2−3

2 ⋅

23 ⋅

2−1)

3

675)

(

(−2)4 ⋅

(−2)−3 ⋅

(−2)0

(−2)3 )−3

676)

(

2−2

22 ⋅

(

2−2)4)

−4

-53-

Page 54: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

677)

20

2 ⋅

2−2

678)

(

(−2)−3

(−2)−2 ⋅

(−2)−2 )4

679)

2 ⋅

2−2

2−4

680)

(

2

24 ⋅

2−3)

2

681)

(

2−1)2

2 ⋅

24

682)

23

(

24)2 ⋅

24

683)

(

(

22)4

2 ⋅

20)

4

684)

(

2−4

2−1

20)

0

685)

2 ⋅

2−3

2−1

686)

2 ⋅

24

(

20)2

-54-

Page 55: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

687)

2−1

20 ⋅

22

688)

(−2)−2 ⋅

(

(−2)3)3

(−2)−3

689)

(

23 ⋅

22

22 )

2

690)

(

(

20 ⋅

23)3

2)0

691)

2 ⋅

(−2)2

(

(−2)0)3

692)

24 ⋅

2−4

(

24)3

693)

(

2 ⋅

24)3

20

694)

23

24 ⋅

(

2−1)0

695)

(−2)2 ⋅

(

(−2)4)0

(−2)−1696)

(

22 ⋅

23

23 )

2

-55-

Page 56: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

697)

(−2)−2 ⋅

(−2)2

(

(−2)2)2

698)

23

2 ⋅

2−2

699)

(

2 ⋅

(−2)−4

(

(−2)2)−2 )

−4

700)

(−2)4 ⋅

(−2)−1

(

(−2)−1)4

701)

24

2−1

(

2−4)2

702)

(

24

2−4

2−3)

2

703)

(

2−1

2−3

2−2)

−1

704)

2 ⋅

2−4

2−2

(

20)2

705)

2 ⋅

24

24 ⋅

23

706)

(

2−2

24 ⋅

22

24 )

−1

-56-

Page 57: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

707)

(

2−4)2

24 ⋅

23

708)

2−3

2 ⋅

(

22)−1

709)

24 ⋅

(

22)4

2710)

(

22)−4

2−1

2−3

711)

(

2−2)4

4712)

(

2 ⋅

22

22 )

3

713)

(

2 ⋅

24

22 )

−3

714)

(

24)−4

2 ⋅

22

715)

2

2−4

(

22)4

716)

2−1

(

22)−2 ⋅

23

-57-

Page 58: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

717)

(

20)−3 ⋅

22

(

2−4)4

718)

(

22 ⋅

2−3)2

24

719)

(

22)0

2 ⋅

2−3

720)

20 ⋅

2−3

(

23)4

721)

(

23)−3

23 ⋅

2−3

722)

23 ⋅

24

(

20)2

723)

(

22

2 ⋅

2−3)

2

724)

(

22)4 ⋅

24

2−4

725)

2 ⋅

2−2

(

23)3

726)

(

2−2

2−4

24)

2

-58-

Page 59: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

727)

23

(

2−1

20)−2

728)

2 ⋅

24

(

23)3

729)

(

(

20)3

2 ⋅

2−1)

4

730)

(

2 ⋅

22)4

2−2

731)

23

(

24)0 ⋅

2−3

732)

(

2 ⋅

(

2−1)−2)

3

2−3

733)

(

23 ⋅

20)4

2−2

734)

(

23)3 ⋅

24 ⋅

2−1

24

735)

(

20 ⋅

20

2−3

24)

4

736)

(

2−4

22

2 ⋅

22 )

3

-59-

Page 60: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

737)

(

2 ⋅

(

22)4

22 ⋅

(

23)0)

4

738)

(

24)3

23 ⋅

20

739)

22 ⋅

22

24

740)

2−4

2−2

22

741)

(

23 ⋅

2−1

(

24)4 )

−3

742)

(

20)−4

22 ⋅

22

743)

2−1

2−1

2−3

744)

(

2−4

23

(

23)−4 )

4

745)

(

2 ⋅

24)4

2746)

(

22 ⋅

2−4

22 )

3

-60-

Page 61: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

747)

(

2−4

24 ⋅

2−3)

−2

748)

24

(

2−1)4 ⋅

22

749)

24

(

23)2 ⋅

2−3

750)

2 ⋅

(

24)0

20

751)

(

2−4

(

23 ⋅

(

2−1)−1)

3)4

752)

(

22)3

24 ⋅

20

753)

22

(

24)−2 ⋅

2−3

754)

2 ⋅

(

2−1)−3

2−4

755)

2 ⋅

24

22

756)

(

2 ⋅

2−3

2)−3

-61-

Page 62: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

757)

(

24)2 ⋅

20

2758)

(

24

2−1

2−4)

4

759)

(

24

23 ⋅

(

23)2)

2

760)

(

20)−1

2−1

2−3

761)

(

2−2

2−3

22 )

−1

762)

2−2

24

(

2−3)3

763)

2−3

2−2

(

2−4)0

764)

(

24)−4 ⋅

(

22)4

20

765)

20

24 ⋅

22 ⋅

(

24)0

766)

(

(

2−1)3

22 ⋅

20 ⋅

2−4)

4

-62-

Page 63: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

767)

(

2−3

2−2

2−1

23)

3

768)

(

24 ⋅

2−1

2−2 )

2

769)

2−3

2 ⋅

(

23)2

770)

(

23)4 ⋅

24

(

24)4

771)

2 ⋅

24

(

2−4)2

772)

23

4

773)

(

24

22 ⋅

2−1)

2

774)

(

24)2

23 ⋅

24

775)

2 ⋅

20

(

22)2

776)

(

23)3

23 ⋅

(

2−3)−1

-63-

Page 64: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

777)

2

(

2−1

22)0

778)

24 ⋅

24

(

2−1)4

779)

2−1

22

(

22)−2

780)

2

(

2−2)2 ⋅

20

781)

(

2−3)3

2 ⋅

22

782)

24

(

20)4 ⋅

22

783)

(

2−1

2−4

2−4 )

3

784)

(

23)4 ⋅

24

2

785)

(

24

22 ⋅

24)

−4

786)

2

20 ⋅

(

2−4)4

-64-

Page 65: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

787)

24 ⋅

2−2

(

20)−4

788)

(

23)−4 ⋅

23

22

789)

4

(

20)3

790)

(

2 ⋅

24

2−4 )

−3

791)

22

24 ⋅

23

792)

(

22)−2

22 ⋅

20

793)

(

2 ⋅

2−2

2−4 )

−3

794)

(

22

23 ⋅

2−2)

3

795)

(

2−2)−1

2−3

24

796)

(

22)−2 ⋅

22 ⋅

20

22

-65-

Page 66: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

797)

(

2−2)−1 ⋅

2−1

20

798)

(

23 ⋅

20

(

23)2 ⋅

24)

−1

799)

22 ⋅

24

(

22 ⋅

2−1)2

800)

2 ⋅

22

(

24)2

-66-

Page 67: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

MATHEMANIA.COM

Properties of exponents - Numeric expressions

Simplify result to only positive exponents:

1)

40 ⋅

42

42

2)

42 ⋅

40

42

3)

−4 ⋅

(−4)4

(−4)5

4)

(−4)4 ⋅

(−4)2 ⋅

(−4)2

(−4)8

5)

(−3)4 ⋅

(−3)2 ⋅

(−3)4

(−3)10

6)

43 ⋅

43

46

7)

−4 ⋅

(−4)0 ⋅

(−4)4

(−4)5

8)

−2 ⋅

(−2)3 ⋅

(−2)4

(−2)8

9)

3 ⋅

30

3

10)

3 ⋅

32

33

11)

30 ⋅

33

33

12)

20 ⋅

22

22

-1-

Page 68: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

13)

32 ⋅

33

35

14)

(−4)2 ⋅

(−4)4

(−4)6

15)

23 ⋅

24

27

16)

4 ⋅

43

44

17)

(−3)3 ⋅

(−3)3

(−3)6

18)

(−3)0 ⋅

(−3)4

(−3)4

19)

20 ⋅

24

24

20)

−2 ⋅

(−2)4

(−2)5

21)

4 ⋅

44

45

22)

(−2)3 ⋅

(−2)2

(−2)5

23)

−2 ⋅

(−2)0

−2

24)

(−2)4 ⋅

(−2)2

(−2)6

25)

−4 ⋅

(−4)2

(−4)3

26)

3 ⋅

34

35

-2-

Page 69: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

27)

3 ⋅

34

35

28)

−3 ⋅

(−3)3

(−3)4

29)

(−2)3 ⋅

(−2)3

(−2)6

30)

40 ⋅

44

44

31)

16 ⋅

(−4)2

(−4)4

32)

(−4)3 ⋅

(−4)2 ⋅

(−4)0

(−4)5

33)

2 ⋅

22 ⋅

23

26

34)

3 ⋅

34 ⋅

32

37

35)

2 ⋅

24

25

36)

4 ⋅

44 ⋅

44

49

37)

34 ⋅

30

34

38)

43 ⋅

40

43

39)

30 ⋅

32

32

40)

44 ⋅

42

46

-3-

Page 70: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

41)

−2 ⋅

(−2)3

(−2)4

42)

23 ⋅

22

25

43)

34 ⋅

32

36

44)

(−3)0 ⋅

(−3)3

(−3)3

45)

(−3)3 ⋅

(−3)2

(−3)5

46)

24 ⋅

24

28

47)

−2 ⋅

(−2)2

(−2)3

48)

−3 ⋅

(−3)0

−3

49)

−2 ⋅

(−2)2

(−2)3

50)

−4 ⋅

(−4)0

−4

51)

2 ⋅

20 ⋅

23

24

52)

(−4)0 ⋅

(−4)3

(−4)3

53)

16 ⋅

(−4)3

(−4)5

54)

20 ⋅

20

1

-4-

Page 71: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

55)

(−2)3 ⋅

(−2)3 ⋅

(−2)2

(−2)8

56)

(−4)4 ⋅

(−4)3

(−4)7

57)

(−3)4 ⋅

(−3)4

(−3)8

58)

20 ⋅

23

23

59)

(−3)2 ⋅

(−3)0

(−3)2

60)

−3 ⋅

(−3)0

−3

61)

4 ⋅

40

4

62)

2 ⋅

22

23

63)

42 ⋅

42

44

64)

(−2)0 ⋅

(−2)3

(−2)3

65)

(−2)2 ⋅

(−2)3

(−2)5

66)

33 ⋅

34

37

67)

(−3)2 ⋅

(−3)3

(−3)5

68)

(−3)3 ⋅

(−3)4

(−3)7

-5-

Page 72: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

69)

34 ⋅

33

37

70)

16 ⋅

43

45

71)

2 ⋅

24 ⋅

20

25

72)

9 ⋅

33

35

73)

(−4)4 ⋅

(−4)3 ⋅

(−4)3

(−4)10

74)

(−2)3 ⋅

(−2)4 ⋅

(−2)4

(−2)11

75)

−2 ⋅

(−2)3

(−2)4

76)

−2 ⋅

(−2)4

(−2)5

77)

−4 ⋅

(−4)0

−4

78)

(−3)2 ⋅

(−3)4

(−3)6

79)

(−3)3 ⋅

(−3)0

(−3)3

80)

33 ⋅

32

35

81)

9 ⋅

(−3)3

(−3)5

82)

(−3)2 ⋅

(−3)2 ⋅

(−3)3

(−3)7

-6-

Page 73: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

83)

4 ⋅

(−2)3

(−2)5

84)

4 ⋅

40 ⋅

44

45

85)

3 ⋅

33 ⋅

32

36

86)

−4 ⋅

(−4)4

(−4)5

87)

−4 ⋅

(−4)2

(−4)3

88)

2 ⋅

22

23

89)

22 ⋅

23

25

90)

(−4)2 ⋅

(−4)3

(−4)5

91)

43 ⋅

42

45

92)

(−3)4 ⋅

(−3)3

(−3)7

93)

33 ⋅

30

33

94)

44 ⋅

44

48

95)

32 ⋅

33 ⋅

34

39

96)

−4 ⋅

(−4)4 ⋅

(−4)3

(−4)8

-7-

Page 74: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

97)

(−4)4 ⋅

(−4)4 ⋅

(−4)2

(−4)10

98)

−3 ⋅

(−3)2 ⋅

(−3)2

(−3)5

99)

(−2)2 ⋅

(−2)2

(−2)4

100)

32 ⋅

32

34

101)

(−4)3 ⋅

(−4)7 ⋅

(−4)−8

(−4)2

102)

6 ⋅

65 ⋅

68

614

103)

−4 ⋅

(−4)2 ⋅

(−4)−8

1

(−4)5

104)

(−5)6 ⋅

(−5)−7 ⋅

(−5)7

(−5)6

105)

33 ⋅

32

35

106)

(−2)2 ⋅

(−2)4

(−2)6

107)

(−3)−6 ⋅

(−3)−5

1

(−3)11

108)

−4 ⋅

(−4)−1

1

109)

(−7)−4 ⋅

(−7)−5

1

(−7)9

110)

76 ⋅

7−6

1

-8-

Page 75: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 76: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

125)

(−3)2 ⋅

(−3)5

(−3)7

126)

(−7)−4 ⋅

(−7)0

1

(−7)4

127)

55 ⋅

53

58

128)

80 ⋅

83

83

129)

(−3)7 ⋅

(−3)−8

1

−3

130)

7−7

7−1

1

78

131)

−4 ⋅

(−4)6 ⋅

(−4)2

(−4)9

132)

(−3)−8 ⋅

(−3)5 ⋅

(−3)−1

1

(−3)4

133)

−8 ⋅

(−8)−1 ⋅

(−8)−1

1

−8

134)

(−7)0 ⋅

(−7)2 ⋅

(−7)−1

−7

135)

(−2)0 ⋅

(−2)5

(−2)5

136)

(−3)3 ⋅

(−3)4

(−3)7

137)

(−7)−6 ⋅

(−7)2

1

(−7)4

138)

−4 ⋅

(−4)7

(−4)8

-10-

Page 77: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

139)

4−3

4−6

1

49

140)

6−3

62

1

6

141)

5−2

5−6

1

58

142)

−6 ⋅

(−6)3

(−6)4

143)

6−7

68

6

144)

2−4

2−6

1

210

145)

(−7)−4 ⋅

(−7)8

(−7)4

146)

7−2

77

75

147)

24 ⋅

27

211

148)

4−1

47

46

149)

(−6)4 ⋅

(−6)−3

−6

150)

(−7)0 ⋅

(−7)−4

1

(−7)4

151)

47 ⋅

44

411

152)

78 ⋅

74

712

-11-

Page 78: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

153)

74 ⋅

75

79

154)

30 ⋅

3−6

1

36

155)

54 ⋅

50

54

156)

(−6)7 ⋅

(−6)−8

1

−6

157)

4−8

42

1

46

158)

8 ⋅

80

8

159)

−4 ⋅

(−4)4 ⋅

(−4)−2

(−4)3

160)

−6 ⋅

(−6)0 ⋅

(−6)6

(−6)7

161)

(−7)0 ⋅

(−7)4 ⋅

(−7)5

(−7)9

162)

8−6

80 ⋅

80

1

86

163)

57 ⋅

50

57

164)

67 ⋅

68 ⋅

65

620

165)

−3 ⋅

(−3)−2

1

−3

166)

7−7

7−4

1

711

-12-

Page 79: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

167)

40 ⋅

4−5

1

45

168)

(−6)6 ⋅

(−6)7

(−6)13

169)

4 ⋅

42

43

170)

8 ⋅

82

83

171)

4 ⋅

46

47

172)

(−5)−3 ⋅

(−5)8

(−5)5

173)

(−8)−2 ⋅

(−8)7

(−8)5

174)

(−2)−1 ⋅

(−2)7

(−2)6

175)

(−3)5 ⋅

(−3)−2

(−3)3

176)

56 ⋅

54

510

177)

4 ⋅

46

47

178)

83 ⋅

8−3

1

179)

(−6)2 ⋅

(−6)−2

1

180)

(−8)0 ⋅

(−8)3

(−8)3

-13-

Page 80: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

181)

(−2)7 ⋅

(−2)4

(−2)11

182)

53 ⋅

55

58

183)

83 ⋅

88

811

184)

76 ⋅

7−7

1

7

185)

2 ⋅

2−7

1

26

186)

47 ⋅

4−8

1

4

187)

6 ⋅

64

65

188)

(−8)6 ⋅

(−8)6 ⋅

(−8)5

(−8)17

189)

(−7)5 ⋅

(−7)0

(−7)5

190)

20 ⋅

2−4

20

1

24

191)

(−8)2 ⋅

(−8)8 ⋅

(−8)0

(−8)10

192)

(−5)0 ⋅

(−5)4

(−5)4

193)

64 ⋅

62 ⋅

65

611

194)

−5 ⋅

(−5)5

(−5)6

-14-

Page 81: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

195)

(−6)−7 ⋅

(−6)0

1

(−6)7

196)

(−7)0 ⋅

(−7)3

(−7)3

197)

74 ⋅

72

76

198)

4−5

40

1

45

199)

(−2)3 ⋅

(−2)7

(−2)10

200)

22 ⋅

28

210

201)

100 ⋅

108

108

202)

59 ⋅

54

513

203)

7−5

77

72

204)

8−10

810

1

205)

107 ⋅

107

1014

206)

39 ⋅

34

313

207)

2−6

2−3

1

29

208)

5 ⋅

56

57

-15-

Page 82: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

209)

8−4

89

85

210)

45 ⋅

4−10

1

45

211)

6 ⋅

65

66

212)

96 ⋅

94

910

213)

6 ⋅

65

66

214)

64 ⋅

67

611

215)

53 ⋅

5−2

5

216)

5−1

58

57

217)

83 ⋅

8−3

1

218)

2−6

210

28

212

219)

25 ⋅

23 ⋅

28

216

220)

84 ⋅

80 ⋅

80

84

221)

27 ⋅

2−5

20

22

222)

210

22

212

-16-

Page 83: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

223)

4 ⋅

4−9

1

48

224)

60 ⋅

64

64

225)

6−1

60

1

6

226)

3−7

39

32

227)

10 ⋅

1010

1011

228)

68 ⋅

69

617

229)

97 ⋅

9−2

95

230)

7−10

72

1

78

231)

4−6

410

44

232)

7−1

7−5

1

76

233)

58 ⋅

50

58

234)

55 ⋅

55

510

235)

10−5

105

1

236)

9 ⋅

90

9

-17-

Page 84: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

237)

34 ⋅

310

314

238)

5−3

5−10

1

513

239)

43 ⋅

4−1

42

240)

75 ⋅

79

714

241)

92 ⋅

93

95

242)

2−7

210

23

243)

5−2

56

54

244)

10 ⋅

10−7

1

106

245)

68 ⋅

62

610

246)

33 ⋅

35

38

247)

8−6

8−4

1

810

248)

4 ⋅

43 ⋅

4−3

4

249)

28 ⋅

2−4

20

24

250)

76 ⋅

7−10

70

1

74

-18-

Page 85: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

251)

7 ⋅

70 ⋅

72

73

252)

96 ⋅

93 ⋅

99

918

253)

10−8

108

1

254)

67 ⋅

67

614

255)

310

3−3

37

256)

47 ⋅

42

49

257)

8−2

85

83

258)

66 ⋅

66

612

259)

910

90

910

260)

70 ⋅

70

1

261)

9−6

9−9

1

915

262)

33 ⋅

3−10

1

37

263)

30 ⋅

3−2

1

32

264)

58 ⋅

55

513

-19-

Page 86: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

265)

79 ⋅

78

717

266)

9−7

90

1

97

267)

9 ⋅

96

97

268)

62 ⋅

68

610

269)

90 ⋅

93

93

270)

710

72

712

271)

82 ⋅

89

811

272)

410

45

415

273)

39 ⋅

3−9

1

274)

8−2

8−8

1

810

275)

63 ⋅

69

612

276)

80 ⋅

8−1

1

8

277)

88 ⋅

89

817

278)

57 ⋅

50 ⋅

57

514

-20-

Page 87: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

279)

4−4

4−2

1

46

280)

94 ⋅

96 ⋅

90

910

281)

7−1

74 ⋅

70

73

282)

85 ⋅

83

88

283)

100 ⋅

103

103

284)

94 ⋅

99

913

285)

6−1

63 ⋅

6−10

1

68

286)

210

2−5

25

287)

74 ⋅

710

714

288)

40 ⋅

42

42

289)

2−5

210

25

290)

5−1

57

56

291)

90 ⋅

97

97

292)

83 ⋅

83

86

-21-

Page 88: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

293)

64 ⋅

60

64

294)

32 ⋅

32

34

295)

103 ⋅

100

103

296)

9−3

9−7

1

910

297)

710

7−10

1

298)

30 ⋅

33

33

299)

5 ⋅

510

511

300)

5−8

50

1

58

301)

62 ⋅

64

66

302)

3−2

38

36

303)

96 ⋅

98

914

304)

87 ⋅

8−3

84

305)

5−1

510

59

306)

9−9

9−6

1

915

-22-

Page 89: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

307)

4−5

43

1

42

308)

4 ⋅

40

4

309)

3 ⋅

3−9

39

3

310)

29 ⋅

2−8

20

2

311)

2 ⋅

2−7

2−6

1

212

312)

4−5

4−3

40

1

48

313)

39 ⋅

3−6

32

35

314)

62 ⋅

69

611

315)

910

9−2

98

316)

2 ⋅

23

24

317)

20 ⋅

26

26

318)

1010

103

1013

319)

5−5

5−5

1

510

320)

8−1

85

84

-23-

Page 90: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

321)

38 ⋅

3−8

1

322)

9−4

910

96

323)

6−9

62

1

67

324)

8−7

85

1

82

325)

77 ⋅

79

716

326)

100 ⋅

10−1

1

10

327)

49 ⋅

44

413

328)

3−6

36

1

329)

3−4

30

1

34

330)

66 ⋅

6−4

62

331)

60 ⋅

60

1

332)

92 ⋅

96

98

333)

25 ⋅

20

25

334)

44 ⋅

4−7

1

43

-24-

Page 91: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

335)

10−1

105

104

336)

23 ⋅

2−10

1

27

337)

20 ⋅

27

27

338)

6−6

60

1

66

339)

72 ⋅

70 ⋅

70

72

340)

510

5−3

50

57

341)

85 ⋅

85

810

342)

9−6

97 ⋅

92

93

343)

810

8−1

89

818

344)

5−6

510

54

345)

77 ⋅

76 ⋅

78

721

346)

89 ⋅

84

813

347)

10 ⋅

103

104

348)

37 ⋅

3−10

1

33

-25-

Page 92: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

349)

70 ⋅

76

76

350)

9−8

98

1

351)

27 ⋅

2−2

25

352)

8 ⋅

88

89

353)

56 ⋅

58

514

354)

45 ⋅

45

410

355)

109 ⋅

10−5

104

356)

5−3

5−6

1

59

357)

75 ⋅

75

710

358)

43 ⋅

46

49

359)

100 ⋅

10−8

1

108

360)

33 ⋅

32

35

361)

67 ⋅

62

69

362)

102 ⋅

109

1011

-26-

Page 93: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

363)

72 ⋅

7−1

7

364)

3−1

3−2

1

33

365)

70 ⋅

7−4

1

74

366)

67 ⋅

60

67

367)

9−4

90

1

94

368)

3−8

3−5

1

313

369)

610

63

613

370)

20 ⋅

2−8

1

28

371)

6 ⋅

63 ⋅

6−9

1

65

372)

10 ⋅

109 ⋅

100

1010

373)

7 ⋅

76 ⋅

74

711

374)

6−2

64 ⋅

64

66

375)

47 ⋅

410

417

376)

33 ⋅

3−1

32

-27-

Page 94: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

377)

67 ⋅

64

611

378)

7−4

74

1

379)

610

6−7

63

380)

45 ⋅

4−4

4

381)

9−9

97

1

92

382)

25 ⋅

23

28

383)

63 ⋅

6−10

1

67

384)

3 ⋅

39

310

385)

70 ⋅

77

77

386)

49 ⋅

4−8

4

387)

46 ⋅

45

411

388)

52 ⋅

510

512

389)

7 ⋅

7−3

1

72

390)

9−6

98

92

-28-

Page 95: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

391)

32 ⋅

3−6

1

34

392)

2 ⋅

2−3

1

22

393)

8−1

87

86

394)

39 ⋅

34

313

395)

4 ⋅

4−8

1

47

396)

104 ⋅

104

108

397)

70 ⋅

710

710

398)

6−4

6−9

1

613

399)

25 ⋅

25

210

400)

210

20

210

401)

(−2)2 ⋅

(

(−2)0)3

(−2)2

402)

(

(−2)0)−3

(−2)2

(−2)2

-29-

Page 96: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

403)

−2 ⋅

(

(−2)−1)4

1

(−2)3

404)

(

24)−3 ⋅

22

1

210

405)

(

22)−2 ⋅

23 ⋅

2−2

1

23

406)

(−2)3 ⋅

(−2)−2 ⋅

(−2)−4

1

(−2)3

407)

23 ⋅

2−3

(

2−2)0

1

408)

(

2−3)0 ⋅

(

2−4)−1

24

409)

(

2 ⋅

(

20)0)

2

22

410)

(

2−4

24)4

1

411)

24 ⋅

2−4

1

412)

(−2)3 ⋅

(−2)4

(−2)7

413)

(−2)2 ⋅

(

(−2)2)4

(−2)10

414)

−2 ⋅

(−2)−2

1

−2

-30-

Page 97: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 98: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

427)

(

23)3 ⋅

2−2

27

428)

23 ⋅

(

23)−3

1

26

429)

(

(−2)3)2

(−2)0

(−2)6

430)

42

24

431)

(

2−2)4 ⋅

24

1

24

432)

(

2 ⋅

24)−4

1

220

433)

(

23)−4 ⋅

2−1

1

213

434)

(

(−2)3)2

(

(−2)−1)2

(−2)0

(−2)4

435)

(

(−2)−1)2

(−2)3 ⋅

(−2)4

(−2)5

436)

2 ⋅

(

24)2

29

437)

(

22 ⋅

2−3)−3 ⋅

2−3

1

438)

2 ⋅

(

24)−3

1

211

-32-

Page 99: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

439)

(

24)−1 ⋅

20

1

24

440)

(−2)0 ⋅

(−2)−1

1

−2

441)

(

20 ⋅

(

24)4)

4

264

442)

(

−2 ⋅

(−2)−1)4

1

443)

2 ⋅

(

2−2)−4

29

444)

(

(−2)−4)−2

(

(−2)−1)2

(−2)6

445)

(−2)3 ⋅

(

(−2)3)0

(−2)3

446)

(−2)−3 ⋅

(−2)−2

1

(−2)5

447)

(

(−2)−3)−1

(

(−2)0)3

(−2)3

448)

(

2−1)4 ⋅

2−4

1

28

449)

(−2)4 ⋅

(

(−2)2)2

(−2)8

450)

(

(−2)3 ⋅

(−2)4)3

(−2)21

-33-

Page 100: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

451)

(

(−2)2)−2

(−2)0

1

(−2)4

452)

(−2)−3 ⋅

(

(−2)0)−1

1

(−2)3

453)

(

(

(−2)−4)3

(−2)3)2

1

(−2)18

454)

23 ⋅

22

25

455)

(

(−2)−4)2

(

(−2)−1)3

1

(−2)11

456)

(

20 ⋅

20)4

1

457)

2 ⋅

(

22)−2

1

23

458)

(

23)4 ⋅

2−3

29

459)

20 ⋅

(

24)4

216

460)

(

23)0 ⋅

23

23

461)

(

2−1)−4 ⋅

20

24

462)

(

(−2)−3 ⋅

(−2)4)−3

1

(−2)3

-34-

Page 101: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

463)

(−2)2 ⋅

(−2)4 ⋅

(

(−2)−2)0

(−2)6

464)

(

2 ⋅

2−2)3

1

23

465)

2 ⋅

(

22)−3 ⋅

23

1

22

466)

(

(−2)4 ⋅

(

(−2)3)3)

2

(−2)26

467)

(

(−2)4)3

(−2)−4 ⋅

(−2)2

(−2)10

468)

(−2)3 ⋅

(

(−2)2)−3

1

(−2)3

469)

(−2)2 ⋅

(

(−2)−4)−4

(−2)18

470)

(

22)−1 ⋅

2−1

1

23

471)

2−1

23

22

472)

(

(−2)3)4

(−2)3

(−2)15

473)

(

(−2)4)−1

(−2)−1

1

(−2)5

474)

(

−2 ⋅

(−2)2)3

(−2)9

-35-

Page 102: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

475)

(

(−2)4)2

(

(−2)−4)4

1

(−2)8

476)

22 ⋅

(

2−2)−2

26

477)

(

−2 ⋅

(−2)2)3

(−2)9

478)

(

23 ⋅

22)−2

1

210

479)

2−4

(

24)2

24

480)

2−1

(

22)2

23

481)

−2 ⋅

(

(−2)−2)−2

(−2)5

482)

24 ⋅

(

23)3

213

483)

(

24)−1 ⋅

24

1

484)

24 ⋅

(

2−3)3

1

25

485)

(

(−2)2)−3

(

(−2)4)3

(−2)6

486)

(

2−1)−3 ⋅

2−3

1

-36-

Page 103: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 104: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

499)

(

2−1

23)−3

1

26

500)

(−2)−1 ⋅

(−2)0

1

−2

501)

(

2−2)−1 ⋅

23

25

502)

(

2−1)3 ⋅

2−4

1

27

503)

24 ⋅

(

2−3)3

1

25

504)

22 ⋅

(

22)−4

1

26

505)

(

20)4 ⋅

2−2

1

22

506)

(

20)−2 ⋅

(

2−4)3

1

212

507)

20 ⋅

(

23)2

26

508)

2 ⋅

(

20)4

2

509)

(

24 ⋅

2−3)2

22

510)

(

2 ⋅

2−4)−2

26

-38-

Page 105: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

511)

22 ⋅

(

20)2

22

512)

(

2−1)2 ⋅

(

22)3

24

513)

22 ⋅

(

2−4)−4

218

514)

(

22)4 ⋅

(

2−4)0

28

515)

23 ⋅

23

26

516)

20 ⋅

(

2−1)0

1

517)

2−4

(

22)−4

1

212

518)

(

22)−2 ⋅

2−2

1

26

519)

(

24)3 ⋅

(

22)2

216

520)

(

2−4

24)0

1

521)

22 ⋅

(

22)2

26

522)

(

22)4 ⋅

24

212

-39-

Page 106: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

523)

(

2−4

20)0

1

524)

(

2−3)3 ⋅

2−3

24

1

28

525)

(

23)−1 ⋅

23 ⋅

20

1

526)

(

2−1)3 ⋅

2−3

2−2

1

28

527)

(

24)2 ⋅

24

212

528)

24 ⋅

(

24)2

212

529)

(

20)4 ⋅

2−1

1

2

530)

(

22)4 ⋅

23

211

531)

(

22 ⋅

2−2)−2

1

532)

(

2 ⋅

22)2

26

533)

(

24)3 ⋅

20

212

534)

2 ⋅

(

24)0

2

-40-

Page 107: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

535)

2 ⋅

(

2−4)2

1

27

536)

24 ⋅

(

23)−1

2

537)

(

22)−4 ⋅

23

1

25

538)

23 ⋅

(

23)3

212

539)

(

24)4 ⋅

(

24)3

228

540)

(

2 ⋅

23)2

28

541)

2−1

22

2

542)

2 ⋅

(

22)0

2

543)

(

2−3)2 ⋅

23

1

23

544)

(

24 ⋅

2−2)0

1

545)

24 ⋅

(

24)4

220

546)

(

2−4)−2 ⋅

22

210

-41-

Page 108: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

547)

20 ⋅

(

22)0

1

548)

(

23 ⋅

(

2−4)−1)

−4

1

228

549)

(

22 ⋅

23)4

220

550)

(

22)3 ⋅

2−3

23

551)

(

24)0 ⋅

(

22)0

1

552)

(

(

23)4 ⋅

2−4)

4

232

553)

22 ⋅

23

25

554)

(

2 ⋅

23)−1

1

24

555)

2 ⋅

(

22)−1 ⋅

23

22

556)

(

22 ⋅

2−3)−3 ⋅

23

26

557)

2−1

(

2−3)2 ⋅

24

1

23

558)

(

2 ⋅

(

23)−2)

0

1

-42-

Page 109: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

559)

20 ⋅

20

1

560)

2−4

(

2−4)3

1

216

561)

(

22 ⋅

22)0

1

562)

(

22)2 ⋅

2−3

2

563)

(

20 ⋅

2−3)4

1

212

564)

2−2

(

22)−4

1

210

565)

2−1

(

2−3)0

1

2

566)

(

2 ⋅

24)2

210

567)

(

23)0 ⋅

23

23

568)

(

24 ⋅

2−4)4

1

569)

(

23)4 ⋅

24

216

570)

23 ⋅

(

24)2

211

-43-

Page 110: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

571)

2−3

(

22)2

2

572)

(

2−1)3 ⋅

20

1

23

573)

2−3

24

2

574)

22 ⋅

(

24)−4

1

214

575)

(

2−4

2−4)0

1

576)

(

24 ⋅

22)3

218

577)

(

24 ⋅

20)4

216

578)

(

(

20)−1 ⋅

24)

2

28

579)

(

2−1)−4 ⋅

20

24

580)

2−2

(

2−2)3

1

28

581)

24 ⋅

(

22)4

212

582)

22 ⋅

(

2−1)−4 ⋅

2−3

23

-44-

Page 111: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

583)

(

2−1

2−2)−2 ⋅

(

23)4

218

584)

(

2−4)2 ⋅

2−4

1

212

585)

20 ⋅

(

2−3)0

1

586)

(

24)3 ⋅

2−3

29

587)

(

2 ⋅

(

23)0)

−1

1

2

588)

(

2−1

24)−2

1

26

589)

(

2 ⋅

2−1)0

1

590)

23 ⋅

(

20)3

23

591)

(

2−2)4 ⋅

20

1

28

592)

2 ⋅

(

24)−1

1

23

593)

2−2

23

2

594)

(

24)−4 ⋅

(

22)3

1

210

-45-

Page 112: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

595)

2−1

2−1

1

22

596)

(

20)4 ⋅

22

22

597)

(

2−2

23)3

23

598)

(

2−1

23)2

24

599)

20 ⋅

(

2−1)−1

2

600)

(

20 ⋅

2−3)−3

29

601)

20 ⋅

(

2−3)−3

2

28

602)

2−3

(

24)−3 ⋅

24

25

603)

(

24)2 ⋅

24

2−3

215

604)

24

20 ⋅

(

22)4

1

24

605)

(

(−2)−3)−2

(−2)3

−2

(−2)8

606)

20

2−3

(

23)3

1

26

-46-

Page 113: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

607)

22

2 ⋅

(

2−2)4

29

608)

(

2−4

2−1

24 )

0

1

609)

(

24

2 ⋅

2−4)

0

1

610)

(−2)4 ⋅

(−2)0

(

(−2)2)3

1

(−2)2

611)

2 ⋅

2−2

22

(

22)−4

29

612)

(

22 ⋅

22

24 )

4

1

613)

23

22 ⋅

(

20 ⋅

2−2)4

29

614)

(−2)4 ⋅

(−2)−1

(−2)0

(−2)3

615)

(

(−2)−2)−2

(−2)−3 ⋅

(−2)2 ⋅

(−2)−1

(−2)6

616)

(

(−2)−4)3

(−2)−1 ⋅

(−2)−2

1

(−2)9

-47-

Page 114: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

617)

(

20 ⋅

2−2

2)−1

23

618)

2−4

(

2−1)−3

(

2−1)4

23

619)

(−2)0

(−2)−2 ⋅

(−2)2

1

620)

(

(−2)4 ⋅

(−2)−3

−2)2

1

621)

22 ⋅

(

22)−3

2

1

25

622)

(

(−2)4 ⋅

(−2)4

(

(−2)−4)4 )

0

1

623)

(

(−2)−2

(−2)4 ⋅

(−2)3 )3

1

(−2)27

624)

(

(

2−3)−1 ⋅

22

2−1 )

2

212

625)

(−2)2 ⋅

(−2)−4

(−2)4

1

(−2)6

626)

(−2)2

(

(−2)2 ⋅

(−2)−2)−1

(−2)2

-48-

Page 115: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

627)

2 ⋅

22

(

2−3)4

215

628)

(

(−2)−4 ⋅

(−2)4)2

(−2)4

1

(−2)4

629)

(−2)−2

−2 ⋅

(−2)−2

1

−2

630)

(

22 ⋅

20

2−4 )

0

1

631)

(

(−2)−4

(

(−2)−4 ⋅

(−2)4)4 )

0

1

632)

(−2)4 ⋅

(−2)2

(−2)−3

(−2)9

633)

(−2)−3

(

(−2)4)−3

(−2)0

(−2)9

634)

(

(−2)−4

(

(

(−2)−4)3

(−2)3)4 )

2

(−2)64

635)

20

22 ⋅

23

1

25

636)

(

24)−4 ⋅

2−2

20

1

218

-49-

Page 116: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

637)

(

2−3

(

2−4)2

(

2−3)4 )

3

23

638)

2 ⋅

(−2)3

(−2)2

(−2)2

639)

(

24)3

2−1

2−3

216

640)

22

22 ⋅

(

2−3)3

29

641)

(

2 ⋅

22

24 )

−1

2

642)

20 ⋅

(

22)2

2−2

24

22

643)

(

(−2)−3 ⋅

(−2)−3

−2)2

1

(−2)14

644)

(−2)4

(−2)2 ⋅

(−2)4 ⋅

(−2)2

1

(−2)4

645)

(

(

(−2)−4)3

(−2)0 ⋅

(

(−2)−2)−3

(−2)2)−2

(−2)40

646)

(

(−2)−4)−3

(−2)4 ⋅

(−2)0

(−2)8

-50-

Page 117: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

647)

(

(−2)0

(−2)−4 ⋅

(−2)4 )0

1

648)

2−1

23

(

24)−2

210

649)

23

20 ⋅

2−2

25

650)

(

(−2)3

(−2)3 ⋅

(−2)−1 )3

(−2)3

651)

(

2−4)3

2−3

2−4

1

25

652)

(−2)3 ⋅

(−2)−4

(

(−2)3)3

1

(−2)10

653)

(−2)3 ⋅

(−2)−4

(

(−2)−2)3

(−2)5

654)

(

(−2)−4

(−2)−3 ⋅

(−2)4 )−3

(−2)15

655)

2−1

(

20)2 ⋅

22

1

23

656)

(

24 ⋅

2−1)4

20

212

-51-

Page 118: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

657)

(

2−4

2−3)3

(

24)−1

1

217

658)

(

(−2)−1

(−2)−1 ⋅

(−2)−2 )3

(−2)6

659)

(

2

(

24)4 ⋅

(

20)4)

4

1

260

660)

(

−2 ⋅

(−2)4)0

(−2)4

1

(−2)4

661)

(−2)2

(−2)3 ⋅

(

(−2)−3)3

(−2)8

662)

(

(−2)0)−1

(−2)−2 ⋅

(−2)4

1

(−2)2

663)

(

24 ⋅

2−4

23 )

−2

26

664)

(−2)3 ⋅

(−2)−4

(

(−2)2)4

1

(−2)9

665)

2 ⋅

(−2)−3

(

(−2)3)0

1

(−2)2

666)

(

2−4

23

23 )

4

1

216

-52-

Page 119: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

667)

(

(−2)2)−1

(−2)2

(−2)2

1

(−2)2

668)

(

2−1)−1

22 ⋅

24

1

25

669)

(

(

22)3 ⋅

22

2)−2

1

214

670)

(

(−2)0)−2

(−2)3 ⋅

(−2)3

1

(−2)6

671)

23

2−1

2−1

25

672)

(

22)3

2−3

24 ⋅

2−3

28

673)

(−2)−3

(

(−2)−1)2

(

(−2)3)4

1

(−2)13

674)

(

2−3

2 ⋅

23 ⋅

2−1)

3

1

218

675)

(

(−2)4 ⋅

(−2)−3 ⋅

(−2)0

(−2)3 )−3

(−2)6

676)

(

2−2

22 ⋅

(

2−2)4)

−4

1

216

-53-

Page 120: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 121: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

687)

2−1

20 ⋅

22

1

23

688)

(−2)−2 ⋅

(

(−2)3)3

(−2)−3

(−2)10

689)

(

23 ⋅

22

22 )

2

26

690)

(

(

20 ⋅

23)3

2)0

1

691)

2 ⋅

(−2)2

(

(−2)0)3

(−2)3

692)

24 ⋅

2−4

(

24)3

1

212

693)

(

2 ⋅

24)3

20

215

694)

23

24 ⋅

(

2−1)0

1

2

695)

(−2)2 ⋅

(

(−2)4)0

(−2)−1

(−2)3

696)

(

22 ⋅

23

23 )

2

24

-55-

Page 122: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

697)

(−2)−2 ⋅

(−2)2

(

(−2)2)2

1

(−2)4

698)

23

2 ⋅

2−2

24

699)

(

2 ⋅

(−2)−4

(

(−2)2)−2 )

−4

1

(−2)4

700)

(−2)4 ⋅

(−2)−1

(

(−2)−1)4

(−2)7

701)

24

2−1

(

2−4)2

213

702)

(

24

2−4

2−3)

2

222

703)

(

2−1

2−3

2−2)

−1

1

24

704)

2 ⋅

2−4

2−2

(

20)2

1

25

705)

2 ⋅

24

24 ⋅

23

1

22

706)

(

2−2

24 ⋅

22

24 )

−1

1

-56-

Page 123: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

707)

(

2−4)2

24 ⋅

23

1

215

708)

2−3

2 ⋅

(

22)−1

1

22

709)

24 ⋅

(

22)4

2

211

710)

(

22)−4

2−1

2−3

1

24

711)

(

2−2)4

4

1

210

712)

(

2 ⋅

22

22 )

3

23

713)

(

2 ⋅

24

22 )

−3

1

29

714)

(

24)−4

2 ⋅

22

1

219

715)

2

2−4

(

22)4

1

23

716)

2−1

(

22)−2 ⋅

23

1

-57-

Page 124: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

717)

(

20)−3 ⋅

22

(

2−4)4

218

718)

(

22 ⋅

2−3)2

24

1

26

719)

(

22)0

2 ⋅

2−3

22

720)

20 ⋅

2−3

(

23)4

1

215

721)

(

23)−3

23 ⋅

2−3

1

29

722)

23 ⋅

24

(

20)2

27

723)

(

22

2 ⋅

2−3)

2

28

724)

(

22)4 ⋅

24

2−4

216

725)

2 ⋅

2−2

(

23)3

1

210

726)

(

2−2

2−4

24)

2

1

24

-58-

Page 125: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47
Page 126: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

737)

(

2 ⋅

(

22)4

22 ⋅

(

23)0)

4

228

738)

(

24)3

23 ⋅

20

29

739)

22 ⋅

22

24

1

740)

2−4

2−2

22

1

24

741)

(

23 ⋅

2−1

(

24)4 )

−3

242

742)

(

20)−4

22 ⋅

22

1

24

743)

2−1

2−1

2−3

2

744)

(

2−4

23

(

23)−4 )

4

244

745)

(

2 ⋅

24)4

2

219

746)

(

22 ⋅

2−4

22 )

3

1

212

-60-

Page 127: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

747)

(

2−4

24 ⋅

2−3)

−2

210

748)

24

(

2−1)4 ⋅

22

26

749)

24

(

23)2 ⋅

2−3

2

750)

2 ⋅

(

24)0

20

2

751)

(

2−4

(

23 ⋅

(

2−1)−1)

3)4

1

264

752)

(

22)3

24 ⋅

20

22

753)

22

(

24)−2 ⋅

2−3

213

754)

2 ⋅

(

2−1)−3

2−4

28

755)

2 ⋅

24

22

23

756)

(

2 ⋅

2−3

2)−3

29

-61-

Page 128: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

757)

(

24)2 ⋅

20

2

27

758)

(

24

2−1

2−4)

4

236

759)

(

24

23 ⋅

(

23)2)

2

1

210

760)

(

20)−1

2−1

2−3

24

761)

(

2−2

2−3

22 )

−1

27

762)

2−2

24

(

2−3)3

211

763)

2−3

2−2

(

2−4)0

1

2

764)

(

24)−4 ⋅

(

22)4

20

1

28

765)

20

24 ⋅

22 ⋅

(

24)0

1

26

766)

(

(

2−1)3

22 ⋅

20 ⋅

2−4)

4

1

24

-62-

Page 129: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

767)

(

2−3

2−2

2−1

23)

3

1

29

768)

(

24 ⋅

2−1

2−2 )

2

210

769)

2−3

2 ⋅

(

23)2

1

210

770)

(

23)4 ⋅

24

(

24)4

1

771)

2 ⋅

24

(

2−4)2

213

772)

23

4

2

773)

(

24

22 ⋅

2−1)

2

26

774)

(

24)2

23 ⋅

24

2

775)

2 ⋅

20

(

22)2

1

23

776)

(

23)3

23 ⋅

(

2−3)−1

23

-63-

Page 130: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

777)

2

(

2−1

22)0

2

778)

24 ⋅

24

(

2−1)4

212

779)

2−1

22

(

22)−2

25

780)

2

(

2−2)2 ⋅

20

25

781)

(

2−3)3

2 ⋅

22

1

212

782)

24

(

20)4 ⋅

22

22

783)

(

2−1

2−4

2−4 )

3

1

23

784)

(

23)4 ⋅

24

2

215

785)

(

24

22 ⋅

24)

−4

28

786)

2

20 ⋅

(

2−4)4

217

-64-

Page 131: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

787)

24 ⋅

2−2

(

20)−4

22

788)

(

23)−4 ⋅

23

22

1

211

789)

4

(

20)3

22

790)

(

2 ⋅

24

2−4 )

−3

1

227

791)

22

24 ⋅

23

1

25

792)

(

22)−2

22 ⋅

20

1

26

793)

(

2 ⋅

2−2

2−4 )

−3

1

29

794)

(

22

23 ⋅

2−2)

3

23

795)

(

2−2)−1

2−3

24

2

796)

(

22)−2 ⋅

22 ⋅

20

22

1

24

-65-

Page 132: Properties of exponents - Numerical expressions · 111) (−2)0 ⋅ (−2)7 112) 6 ⋅ 62113) 43 ⋅ 45 114) (−7)−5 ⋅ (−7)8 115) (−7)5 ⋅ (−7)7 116) 4 ⋅ 47 117) 47

797)

(

2−2)−1 ⋅

2−1

20

2

798)

(

23 ⋅

20

(

23)2 ⋅

24)

−1

27

799)

22 ⋅

24

(

22 ⋅

2−1)2

24

800)

2 ⋅

22

(

24)2

1

25

-66-