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Practice CFor use with the lesson “Define and Use Zero and Negative Exponents”

Evaluate the expression.

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

4. 1 }

1025 5. 526

} 529 6.

8210 }

828

7. 15 1 3 } 5 2 21 8. 32 1 224

} 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? Explain your reasoning. Les

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Algebra 1Chapter Resource Book 7-29

Lesson

7.3

CS10_CC_A1_MECR710730_C7L03PC.indd 29 5/13/11 11:43:08 PM

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Lesson Define and Use Zero and Negative Exponents, continued

24. 2y

} x3

25. 3 }

4 in. 26.

1 }

4 in.;

1 }

2 in.

27. π

} 16

in.2; 3π

} 16

in.2

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

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 cm3;

7π }

8 cm3 c. 4 d. overestimated;

A knitting needle narrows at one end.

Study Guide

1. 1 2. 1 }

625 3. 36 4.

8 }

125 5. 1 6. 81 7.

1 }

16

8. 100,000 9. 625x8z4

} y12 10.

n6p2

} 3m4 11.

s4t }

48r11

Problem Solving Workshop: Mixed Problem Solving

1. a. 3375

} 64

cubic inches

b. power of a quotient property

2. a. Blood (cubic millimeters)

Number of white corpuscles

10 104

100 105

1000 106

10,000 107

100,000 108

b. 103 p 105 5 108 3. No, the mass of a sweet corn seed is 0.1 gram.

4. a. Answers will vary. b. Answers will vary.

5. 2800 6. a. 1022 in. b. 1 cubic inch c. Assum-ing the same thickness, the amount of oil needed to cover a container of water with a surface area of 10x square inches is 10x 2 2 cubic inches.

Challenge Practice

1. Always true 2. Never true 3. Never true

4. Always true 5. Sometimes true; true when a 5 1 and b 5 1, false when a 5 2 and b 5 2.

6. True if a > 1. 7. 1 8. 1 9. 21 10. 9 }

256

Lesson Write and Graph Exponential Growth Functions

Teaching Guide

1. Yes because 384,400 kilometers 5 3.844 3 105 kilometers 2. Yes because 0.000057 meter 5 5.7 3 10–5 meter. 3. Yes because 6,500,000,000 5 6.5 3 109.

Practice Level A

1. C 2. A 3. B 4. 6.4 3 100 5. 8.52 3 101

6. 2.5 3 1021 7. 1.04 3 1021 8. 5.4 3 102

9. 9.1245 3 103 10. 9.5 3 1023 11. 6.3 3 105

12. 3 3 1022 13. 2.396 3 104 14. 4.57 3 1022

15. 4.5 3 1025 16. 52,000 17. 910,000,000

18. 625,000 19. 605 20. 8,125,000

21. 11,130,000,000 22. 0.0047

23. 0.000000016 24. 0.00000445

25. 0.000924 26. 0.0071123 27. 0.000020123

28. 4.5 3 103; 15,625; 21,000; 3 3 104

29. 7.8 3 1026; 0.0006; 0.0012; 2.15 3 102

30. 0.0125; 1.3 3 1022; 6.15 3 1021; 1.765

Algebra 1Chapter Resource Book A3

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