Name ———————————————————————
Date ————————————
Practice A
LESSON
7.3
For use with the lesson “Define and Use Zero and Negative Exponents”
Match the equivalent expressions.
1 }23 2
22
22
1 }32 2
2. 222 + 322
3.
4
B. }
9
9
C. }
4
4. 523
5. 822
6. 225
7. (23)24
8. (29)21
9. 60
1.
1
A. }
36
Evaluate the expression.
10. (25)0
13.
21
1 }34 2
0
1 }16 2
11.
1 }12 2
12.
14.
1 }25 2
15. 022
23
22
16. x25
17. m29
18. 6y23
19. 8a210
20. (3b)24
21. x3y22
22. x24y 3
23. a21b22
24. 2x23y1
4 21
25. Finger Thickness Your friend tells you that her finger is }
inch thick. Evaluate
3
1 2
the expression that represents the thickness of your friend’s finger.
26. Floor Tile The minimum recommended width of the space between 6-inch by
6-inch tiles is 222 inch and the maximum recommended width is 221 inch. Simplify
the expressions for the minimum and maximum widths of the space between the
6-inch by 6-inch floor tiles.
27. Hole Punch Your hole punch makes holes in your paper that have a diameter of
421 inch.
a. Write an expression for the area of one punched hole. Use the formula for the
area of a circle A 5 Ĭr2.
b. Your hole punch makes three holes in a page. Write an expression for the total
area punched out of one sheet of paper.
LESSON 7.3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Simplify the expression. Write your answer using only positive exponents.
Algebra 1
Chapter Resource Book
7-27
1. quotient of powers 2. power of a quotient
38
3. quotient of powers 4. }5 5 3825 5 33
3
3 4
34
86
86
}6 5 81 7. 44 8. 93
5. } 5 }4 6. }
5
4
2
4
4
8 +8
8
57
15
5
1
9. 3 10. (25) 11. (27)4 12. }5 13. }7
4
3
29
x3
14. }9 15. 43 16. y6 17. z1 18. m4 19. }
7
y3
9
13
1
a
20. } 21. }9 22. a. 103 b. 10 c. 102 d. 102
13
z
b
1 2
Practice Level B
1. 66 2. 141 3. (25)5 4. 124 5. 87
(21)6
35
6. }5 7. }
8. 37 9. 48 10. y6 11. z9
4
56
216
243x20
a8
a12
12. }8 13. 2}
14. }
15. }
3
20
z
b
16b
y30
12
28
25
m
81x
32m
16. }
17. } 18. } 19. 103
48
125n27
16y
243n45
3087Ĭ
20. a. 104 b. 103 21. } in.3
2
Practice Level C
87
1. 155 2. 64 3. 2}7 4. 87 5. 510 6. 2105
9
81x24
64a6
a7
m42
}
}
7. 2 7 8. 36 9. }
10. }9
60
b
y
64n
125b
6
11
5
49x
27x
8x
20x14
11. }
12. }6 13. }
14. }
14
15
64y
200y
y
27y13
17
8x
15. 2}
16. x 5 8, y 5 3; Use the properties
9y35
of exponents to write two equations in x and y.
Then solve the system of equations.
Ĭ
9Ĭ
9Ĭ
17. 102 18. 1012 19. } ft3; } ft3; } ft3
6
16
2
Study Guide
81
b7
1. 129 2. (28)4 3. 135 4. w 5 5. }7 6. }4
c
w
27s15
9m2
}
}
7. 12 8. 3 9. 10
t
n
Interdisciplinary Application
1.
t
A(t)
A2
0
1
2
100
50
25
Algebra 1
Chapter Resource Book
3
4
5
12.5 6.25 3.125
y
100
80
60
40
20
0
0 1 2 3 4 5 x
5730-year intervals
3. Answers will vary. Sample answer: The
amount of carbon-14 left in an object after 50,000
or 60,000 years would be so small that detection
would be impossible.
Challenge Practice
1
1. a 5 1 2. b 5 3, or b 5 } 3. x 5 1, y 5 4
3
4. 4 5. 0 6. $65,155.79 7. $63,814.08
8. $265,329.77
Lesson 7.3 Define and Use
Zero and Negative Exponents
Teaching Guide
2+2+2
23
23
1. }3 5 23 2 3 5 20; }3 5 } 5 1
2+2+2
2
2
2
42
4
4+4
2. }2 5 42 2 2 5 40; }2 5 } 5 1
4+4
4
4
5
5
3+3+3+3+3
3
3
}5 5 35 2 5 5 30; }5 5 }} 5 1
3+3+3+3+3
3
3
4
x
+x+x+x
x4
x
}4 5 x4 2 4 5 x0; }4 5 } 5 1
x
+x+x+x
x
x
a0 5 1
1
22
22
2+2
3. }4 5 22 2 4 5 222; }4 5 } 5 }2
2+2+2+2
2
2
2
4
1
4
4
4. }2 5 41 2 2 5 421; }2 5 } 5 }
4+4
4
4
4
2
2
3+3
1
3
3
}5 5 32 2 5 5 323; }5 5 }} 5 }3
3+3+3+3+3
3
3
3
x+x
1
x2
x2
}4 5 x2 2 4 5 x22; }4 5 } 5 }2
x+x+x+x
x
x
x
1
a2n 5 }
an
Practice Level A
1. C
1
1
1
1
2. A 3. B 4. } 5. } 6. } 7. }
125
64
32
81
1
4
8. 2} 9. 1 10. 1 11. 1 12. 36 13. }
9
3
125
6
1
1
14. } 15. undefined 16. }5 17. }9 18. }3
8
x
m
y
y3
8
x3
1
1
19. }
20. }4 21. }2 22. }4 23. }2
a10
81b
y
x
ab
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Practice Level A
2.
Grams of carbon
ANSWERS
Lesson 7.2 Apply Exponent
Properties Involving Quotients,
continued
Lesson 7.3 Define and Use Zero
and Negative Exponents,
continued
Practice Level B
64
1
1
1
1. } 2. } 3. } 4. 1 5. 1 6. 1 7. }
243
1000
64
25
343
1
1
8. } 9. undefined 10. } 11. }
64
100,000
64
6
1
1
1
12. 625 13. }7 14. }4 15. }5 16. }
x
32b
y
81m4
3
x12
d5
a2
17. } 18. }
19. }6 20. 1 21. }
2
5
xy
64y
c3
b4
3 7
xy
1
1
22. x2y4 23. } 24. } 25. a. } in.
6 5
3
20
4x y
4Ĭ
2
b. } in. 26. } cm3 27. a. 1026 m
25
375
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
b. 10215 m c. 1022 m
Practice Level C
1
1
1. } 2. 6561 3. } 4. 100,000 5. 125
243
625
x4y8
x6
1
1
6. } 7. 25 8. } 9. 210 10. }8 11. }
64
4
9
16y
11
y
y10
16
12. }4 13. }
14. 128d 8 15. 2}9
16x
6x
x10
12
11
2y
5x
2 5
16. 81x y
17. }
18. }
19. false; a 5 2;
y2
3x2
225
1
}
5 2 Þ }2 20. true 21. false; a 5 1, b 5 1;
226
1
1
} 5 } Þ 2 5 1 1 1 22. 106 23. a. 2
111
2
7Ĭ
7Ĭ
b. } cm3; } cm3 c. 4 d. overestimated;
2
8
A knitting needle narrows at one end.
Study Guide
8
1
1
1. 1 2. } 3. 36 4. } 5. 1 6. 81 7. }
625
125
16
n6p2
625x8z4
s4t
}
}
8. 100,000 9. }
10.
11.
y12
3m4
48r11
Problem Solving Workshop:
Mixed Problem Solving
3375
1. a. } cubic inches
64
b. power of a quotient property
Blood (cubic
millimeters)
Number of white
corpuscles
10
104
100
105
1000
106
10,000
107
100,000
108
ANSWERS
2y
3
1
1
24. } 25. } in. 26. } in.; } in.
4
4
2
x3
Ĭ
3Ĭ
27. } in.2; } in.2
16
16
2. a.
b. 103 + 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. Assuming 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.
9
6. True if a > 1. 7. 1 8. 1 9. 21 10. }
256
Lesson 7.4 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 1
Chapter Resource Book
A3