Name ——————————————————————— Date ————————————

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28Algebra 1Chapter 8 Resource Book

Evaluate the expression.

1. 325 2. 1023 3. (22)26

4. 50 5. (26)0 6. 14}3 20

7. 15}8 222

8. 17}4 23 9. 025

10. 1022 p 1023 11. 426 p 43 12. 1

}524

Simplify the expression. Write your answer using only positive exponents.

13. x27 14. 6y24 15. (2b)25

16. (23m)24 17. a2b24 18. 3x22y25

19. (4x24y2)23 20. (8mn3)0 21. c23}d25

22. x2}y24 23.

x26}4y5 24.

1}3x23y27

25. Paper A sheet of 67-pound paper has a thickness of 10021 inch.

a. Write and evaluate an expression for the total thickness of 5 sheets of 67-pound paper.

b. Write and evaluate an expression for the total thickness of 23 sheets of 67-pound paper.

26. Frogs A frog egg currently has a radius of 521 centimeter. Write an expression using positive exponents for the volume of the frog egg. Use the formula for the

volume of a sphere V 5 4}3πr3.

27. Metric System The metric system has names for very small lengths.

a. One micrometer is 103 times the length of one nanometer. One nanometer is 1029 meter. Write one micrometer in meters.

b. One femtometer is 103 times the length of one attometer. One attometer is 10218 meter. Write one femtometer in meters.

c. One centimeter is 1010 times the length of one picometer. One picometer is 10212 meter. Write one centimeter in meters.

LESSON

8.3 Practice BFor use with pages 502–508

LE

SS

ON

8.3

Answer Key

Lesson 8.3

Practice Level B

1. 1 } 

243 2.

1 } 

1000 3.

1 } 

64 4. 1 5. 1 6. 1 7.

64 } 

25

8. 343

} 64

9. undefined 10. 1 } 

100,000 11.

1 } 

64

12. 625 13. 1 } 

x7 14.

6 } 

y4 15.

1 } 

32b5 16. 1 } 

81m4

17. a2

} b4

18. 3 } 

x2y5 19.

x12

} 64y6

20. 1 21. d 5

} c3

22. x2y4 23. 1 } 4x6y5

24. x3y7

} 3

25. a. 1 } 

20 in. b.

2 } 

25 in.

26. 4π

} 375

cm3

27. a. 1026 m b. 10215 m c. 1022 m

Name ——————————————————————— Date ————————————

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29Algebra 1

Chapter 8 Resource Book

LESSON

8.3 Practice CFor use with pages 502–508

Evaluate the expression.

1. 324 p 321 2. 924 p 98 3. (521)4

4. 1

}1025 5.

526}529 6.

8210}828

7. 1513}5 221

8. 321224}23 2 9. 4 2 2 p 1 7

}120 2

Simplify the expression. Write your answer using only positive exponents.

10. (4x23y4)22 11. 1

}9x24y28 12.

1}6x4y210

13. 1

}(4x25)22

14. 8

}(22d2)24

15. (2x)24y8

}2x5y23

16. x26y4

}(23x2)24y21

17. 20x3y24

}(2x24y21)2

18. (4x24y7)2

}24x26y2

Tell whether the statement is true or false for all nonzero values of a and b. If it is false, give a counterexample.

19. a25}a26 5

1}a

20. b21}a21 5

a}b

21. 1

}a21 1 b21 5 a 1 b

22. Guitar The world’s smallest guitar is only 1026 meter tall. An average guitar is about 100 meter tall. How many times taller is an average guitar than the world’s smallest guitar?

23. Knitting Needles A size 1 knitting needle has a diameter of about 421 centimeter and a size 8 knitting needle has a diameter of about 221 centimeter.

a. How many times larger is the diameter of a size 8 needle than the diameter of a size 1 needle?

b. Suppose that each needle is 14 inches long. Write expressions for the approximate volume of each size of knitting needle. Use the formula for the volume of a cylinder V 5 πr2h.

c. How many times larger is the approximate volume of a size 8 needle than the approximate volume of a size 1 needle?

d. Are your approximations in part (b) overestimates or underestimates? Explainyour reasoning. L

ES

SO

N 8

.3

Answer Key

Lesson 8.3

Practice Level C

1. 1 } 

243 2. 6561 3.

1 } 

625 4. 100,000 5. 125 6.

1 } 

64 7. 25 8.

1 } 

4 9. 210 10.

x6

} 16y8

11. x4y8

} 9

12. y10

} 6x4

13. 16

} x10

14. 128d8 15. 2  y11

} 16x9

16. 81x2y5 17. 5x11

} y2

18. 2y12

} 3x2

19. false; a 5 2; 225

} 226

5 2 Þ 1 } 

2 20. true 21. false; a 5 1, b 5 1;

1 } 

1 1 1 5

1 } 

2 Þ 2 5 1 1 1

22. 106 23. a. 2 b. 7π

} 2 in.3;

7π } 

8 in.3 c. 4 d. overestimated; A needle narrows at one end.

Name Nar

J40ney no J4atter In 1997, NBC renewed its contract to produce a sitcom for the 1997-1998 season for a cost of $120 million-the most expensive TV series renewal ever recorded. This show also demanded the most money in television history for advertisement-more than $1 million per minute. What is the name of this famous show?

To find out, simplify each problem below using only positive exponents. Find your answers in the list provided and circle the corresponding letters. Unscramble the circled letters to discover the answer.

1. 2x-s 2 • -3X °Y-1 3. 2x-Sy3 4. (7x)O 4xo

5. 8x 6. 8x-3y4 7. -6f4y3 8. (. 6x2y3 ) ° 40x-4 -2xy-s 2x0y 3 ~ -2xy4

-3y6

7 N 2

xS

F 2y3

xS E 8x5

D -3 -y

o .xy4

G -4.xy E 1 -4

R 7-4

B -9x2/

S 1 L -4y9

7

I Answer: ~

~ II

I

I I I

i

I miJ Negative and zero exponents I FS122010 Algebra Made Simple· © Carson-Dellosa I FS12:

---L

8. V = (4, -2), opens down 3. 4. Page 54 9. V = (5, 1), opens up 1. Has many solutions

10. V = (3, -5), opens down 2. Has no solution 4 four 3. Has no solution

4. Has many solutionsPage 43 5. Has no solutionT. x < 10 A. x <!: 19 6. Has many solutionsI. x > -22 O. x > -2

6. 7. Has no solutionM A. x <!: 11 E. x < -14 8. Has no solutionL. x:s 25 E. x < -8 9. Has many solutionsH. x <!: 2 N. x> 47

Bugs BunnyH. x > -3 E. x <!: 6

C. x > -6 N. x:s-2 Page 55 An ace in the hole! 1. Quadrants I, II, III, IV

2. Quadrant IIPage 44 7. 8. 3. Quadrants I, II, III 1. x:s -2 or x > 8 4. Quadrants I, III, IV 2. 1:s x :s 7 5. Quadrants I, II 3. -10 < x < 10 6. Quadrant I4. x < -7 or x <!: 8 7. Quadrants I, IV5. -3:s x < 5 8. Quadrants II, III6. x < 2 or x> 5

10. Thriller (Michael Jackson)7. x <!: 9 or x :s 7

8. x < -3 or x <!: 5 Page 58

x15Michigan 1. 3x5 2. 32x5 3.

4. 30x6 5.• -42x7 6. -x4y7Page 45 7. 72J!3y2 8'. -64x12 9. -3X9y7A. x < 1 or x> 3

X 14 8X1210. y2 11. y3W. -4:s x :s -1 Garfield the CatT. -6 < x < 3 three days

Y. x:s -3 or x <!: 7 Page 59 Page 50

A. -3:s x :s 6 1. x 2. -x/91. (4, 5) 2. (1, 8) 3. (17,10)

D. -11 < x < 3 3. 1 4. 1/(2x)4. (3, 3) 5. (3, -1) 6. (-6, 8)

A. V2:sx:s2 5. 81 y2 6. -3/(xy)7. (3,5) 8. (3,4) 9. (5,2)

data-way 7. (-4x)/(3y3) 8. -2y310. (12, 1) For a tune-up!

9. 9x6 thirty-sixPage 46 Page 51

1. yes 2. no 3. yes Page 60 S. (2, 1) M. (1, 1) L. (3, 10)

4. no 5. yes 6. yes 1. 2/x5 2. -3/yX. (-3,2) I. (6,0) I. (-6, 8)

7. no 8. yes 9. no 3. (2y3)/xS 4. 1/4S. (2, 5) E. (-3, -5)

10. yes 5. 8xS 6. (-4y9)/x4 six miles

six 7. (-3y6)/x4 8. 1 Page 52 SeinfeldPage 47 1. (-2, -2) 2. (-3, 0) 3. (4,0)

1. 2. Page 61 4. (0, 1) 5. (2, -2) 6. (2,3)y

1. 0.00031 7. (-1, -1) 8. (4, -5) 9. (3,7)

2. 804,000John Wayne

;c 3. 0.0046 Page 53 4. 2,000 1. (1, -V2) 2. (-5, 2) 3. (2, 2) 5. 56,200,000 4. (1, 0) 5. (1, 1) 6. (-7,3) 6. 0.00000703 7. (-3, 0) 8. (2, 3) 9. (4,0) 7. 5.62 x 106

seven gold 8. 7.8 X 10-6

losa FS122010 Algebra Made Simple • © Carson-Dellosa

5.

9.