# aat solutions - ch05

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• 7/17/2019 Aat Solutions - Ch05

1/73

Company.

Algebra 2

Worked-Out Solution Key

Prerequisite Skills (p. 328)

1. 23 and 1

2. 4

3. y5 ax21 bx1 c

4.

2

x

y

21

(1, 4)

x51

5.3

x

y

21

x521

2

(2 , 218 )1

2

3

4

6.

1

x

y

21

(22, 8)

x

5

2

2

7. x21 9x1 205 (x1 4)(x1 5)

8. 2x21 5x2 35 (2x2 1)(x1 3)

9. 9x22 645 (3x2 8)(3x1 8)

10. 2x21x1 65 0

x521 6 }}

(1)22 4(2)(6)}}

2(2) 5

21 6}

247}

4 5

21 6i}

47}

4

11. 10x21 13x5 3

10x21 13x2 35 0

(5x2 1)(2x1 3)5 0

5x2 15 0 or 2x1 35 0

5x5 1 or 2x5 23

x51

}

5

or x5 23}

2

12. x21 6x1 25 20

x21 6x2 185 0

x526 6 }}

(6)22 4(1)(218)}}

2(1)

526 6

}

108}

2

526 66

}

3}

2

5 23 63}

3

Lesson 5.1

5.1 Guided Practice (pp. 331333)

1. (42)35 46 Power of a power property

5 4096

2. (28)(28)35 (28)11 3Product of powers property

5 (28)4

5 4096

3. 12}9235

23

}

93 Power of a quotient property

58

}

729

4.6 p1024

}

9 p107 5

6

}

9p102427 Quotient of powers property

56

}

9

p10211

52

}

3 p1011

Negative exponent property

5.x26x5x35x261 51 3 Product of powers property

=x2

6. (7y2z5)(y24z21)5 7y21 (24)z51 (21) Product ofpowers property

5 7y22z4

57z4

}

y2

Negative exponent property

7. 1s3

}

t242

2

5

(s3)2

}

(t24)2

Power of a quotient property

5s6

}

t28

Power of a power property

5s6t8 Negative exponent property

8. 1x4y22

}

x3y6 2

3

5

(x4y22)3

}

(x3y6)3 Power of a quotient property

5x4 p3y22 p3

}

x3 p3y6 p3 Power of a product property

5x12y26

}

x9y18

5x1229y26218 Quotient of powers property

5x3

}

y24

Negative exponent property

5.1 Exercises (pp. 333335)

Skill Practice

1. a.Product of powers property

b.Negative exponent property

c.Power of a product property

2. No, 25.2 is not less then 10; the number should be

2.523 1022.

3. 33p325 3(31 2) Product of powers property

5 35

5 243 4. (422)35 426 Power of a power property

51}

46 Negative exponent property

51

}

4096

Chapter 5

• 7/17/2019 Aat Solutions - Ch05

2/73

Company.

288

Algebra 2

Worked-Out Solution Key

5. (25)(25)45 (25)(11 4) Product of powers property

5 (25)5

5 23125

6. (24)25 28 Power of a power property

5 256

7.52

}

555 5(2 2 5) Quotient of powers property

5 523

51

}

53

Negative exponent property

51

}

125

8. 13}5245

34

}

54

Power of a quotient property

581

}

625

9. 12}7223

5223

}

723 Power of a quotient property

5

73

}

23

Negative exponent property

5343

}

8

10. 93p9215 9(31 (21)) Product of powers property

5 92

5 81

11.34

}

322

5 342 (22) Quotient of powers property

5 36

5 729

12. 12}3225

12}3245 12}32

251 4 Product of powers property

5 12}3221

53

}

2

Negative exponent property

13. 63p60p6255 631 02 5 Product of powers property

5 622

51

}

62

Negative exponent property

51

}

36

14. 111}2225

22511}22210

Power of a power property

5

1210

}

2210 Power of a quotient property

5 210 Negative exponent property

5 1024

15. (4.23 103)(1.53 106)5 (4.23 1.5)(1033 106)

5 6.33 109

16. (1.23 1023)(6.73 1027)5 (1.23 6.7)(10233 1027)

5 8.043 10210

17. (6.33 105)(8.93 10212)5 (6.33 8.9)(1053 10212)

5 56.073 1027

5 5.6073 1013 102 7

5 5.6073 1026

18. (7.23 109)(9.43 108)5 (7.23 9.4)(1093 108)

5 67.683 1017

5 6.7683 1013 1017

5 6.7683 1018

19. (2.13 1024)35 2.133 (1024)3

5 9.2613 10212

20. (4.03 103)45 4.043 (103)4

5 2563 1012

5 2.563 1023 1012

5 2.563 1014

21.8.13 1012

}

5.43 109 5

8.1

}

5.43

1012

}

109

5 1.53 103

22. 1.13 1023

}

5.53 1028

5 1.1

}5.5

3 1023

}1028

5 0.23 105

5 2.03 10213 105

5 2.03 104

23.(7.53 108)(4.53 1024)

}}

1.53 107 5

(7.53 4.5)(1083 1024)

}}

1.53 107

533.753 104

}

1.53 107

53.3753 1013 104

}}

1.53 107

53.3753 105

}

1.53

107

53.375

}

1.5

3105

}

107

5 2.253 1022

24.w22

}

w6 5 w22 2 6 Quotient of powers property

5 w28

51

}

w8

Negative exponent property

25.(22y3)55 (22)5(y3)5 Power of a product property

5 210y15 Power of a power property

5 1024y15

26.(p3q2)215p23q22 Power of a product property

51

}

p3q2 Negative exponent property

27.(w3x22)(w6x21)5 w31 6x221 (21) Product of powersproperty

5 w9x23

5w9

}

x3

Negative exponent

property

Chapter 5, continued

• 7/17/2019 Aat Solutions - Ch05

3/73

Company.

Algebra 2

Worked-Out Solution Key

28.(5s22t4)235 523(s22)23(t4)23 Power of a productproperty

51

}

125

ps22(23)pt4(23) Power of a power

property

51

}

125ps6pt212

5s6

}

125t12

Negative exponent

property

29. 13a3b52235 (3)23(a3)23(b5)23 Power of a productproperty

51

}

27

a3(23)b5(23) Power of a power

property

51

}

27

a29b215

51

}

27a9b15 Negative exponent property

30.x21y2

}

x2y215x2122y22 (21) Quotient of powers property

5x23y3

5y3

}x3

Negative exponent property

31.3c3d

}

9cd215

3

}

9

c32 1d12 (21) Quotient of powers property

5c2d2

}

3

32.4r4s5

}

24r4s255

4

}

24

r42 4s52 (25) Quotient of powers property

51

}

6

r0s10

51

}

6

p1 ps10 Zero exponent property

5

s10

}

6

33.2a3b24

}

3a5b225

2

}

3

a32 5b242 (22) Quotient of powers property

52

}

3

a22b22

52

}

3a2b2

Negative exponent property

34.y11

}

4z3p

8z7

}

y7 5

8y11z7

}

4y7z3

5 2y112 7z72 3 Quotient of powers property

5 2y4z4

35.x2y

2

3

}3y2 p y

2

}x245

x2y2

1

}

3x24y2

Product of powers property

5x22 (24)y2122

}}

3

Quotient of powers property

5x6y23

}

3

5x6

}

3y3

Negative exponent property

36. B;

2x2y

}

6xy215

x22 1y12 (21)

}

3

5xy2

}

3

37. The error is that the exponents were divided and not

subtracted.

x10

}

x2 5x102 2

5x8

38. The error is that the exponents were multiplied instead

x5px35x51 3

5x8

39. The error is that the bases were multiplied.

(23)2p(23)45 (23)6

40.A5

}

3}

4

s2 s5x

}

3

5 }

3}4 1x}322

5

}

3}

4 1x

2

}32

25

}

3x2

}

4 p9

5

}

3x2

}

36

41. v5 r2h r = x h5x

}

2

5 (x)21x}22

5 x2px

}

2

5x3

}

2

42. v5 lpwph l5 2x, w55x

}

3

, h5x

5(2x)15x}32(x)

510x3

}

3

43.x15y12z85x4y7z11p?

x15y12z8

}

x4y7z11

5 ?

x152 4y122 7z82 115 ?

x11y5z235x11y5

}

z3

5 ?

44. 3x3y2512x2y5

}

?

?512x2y5

}

3x3y2

5 4x22 3y52 2

5 4x21y3

54y3

}

x

Chapter 5, continued

• 7/17/2019 Aat Solutions - Ch05

4/73

Company.

290

Algebra 2

Worked-Out Solution Key

45. (a5b4)25 a14b21p?

a5 p2b4 p25 a14b21p?

a10b85 a14b21p?

a10b8

}

a14b215 ?

a102 14p

b82 (21)5 a24b95b9

}

a

45 ?

x12x165 (x4y4)(x8y12)5 (x2y15)(x10y1)5 (x25y7)(x17y9)

47.1}

am5

a0

}

am5 a02 m5 a2m

48.am

}

an5 amp

1}

an

a2np

am5 a2n1 m5 am2 n

Problem Solving

49. Pacific: V5 (1.563 1014)(4.033 103)

5 (1.563 4.03)(10143 103)

5 6.28683 1017meters3

Atlantic: V5 (7.683 1013)(3.933 103)

5 (7.683 3.93)(10133 103)

5 30.1824 3 1016

5 3.018243 1013 1016

5 3.018243 1

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