Chapter Review
Write each expression using exponents.
1. 6 • 6 • 6 • 6 • 6
SOLUTION: The base 6 is a factor 5 times. So, the exponent is 5.
5
6 • 6 • 6 • 6 • 6 = 6
ANSWER: 5
6
2. 4
SOLUTION: The base 4 is a factor 1 time. So, the exponent is 1.
1
4=4
ANSWER: 1
4
3. x • x • x
SOLUTION: The base x is a factor 3 times. So the exponent is 3.
3
x • x • x = x
ANSWER: x
3
4. f • f • g • g • g • g
SOLUTION: ANSWER: 2 4
f g
Evaluate each expression.
5
5. 3
SOLUTION: ANSWER: 243
3
6. 2 • 4
SOLUTION: eSolutions Manual - Powered by Cognero
Page 1
ANSWER: 243
Chapter Review
3
6. 2 • 4
SOLUTION: ANSWER: 128
3
7. (–4)
SOLUTION: ANSWER: –64
0
8. 4 • 5
SOLUTION: ANSWER: 5
Evaluate each expression if w =
, x = 4, y = 1, and z = –5.
2
9. x – 6
SOLUTION: ANSWER: 10
3
10. w + y
2
SOLUTION: eSolutions Manual - Powered by Cognero
ANSWER: Page 2
ANSWER: 10
Chapter Review
3
10. w + y
2
SOLUTION: ANSWER: 3
11. 2(y + z )
SOLUTION: ANSWER: –248
4 2
12. w x yz
SOLUTION: ANSWER: or
5
13. Adult humans have 2 teeth. How many teeth do adults have?
SOLUTION: So, adult humans have 32 teeth.
ANSWER: 32 teeth
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3
14. Xander ran a total of 5 kilometers last month. How many kilometers did he run?
Page 3
ANSWER: Chapteror Review
5
13. Adult humans have 2 teeth. How many teeth do adults have?
SOLUTION: So, adult humans have 32 teeth.
ANSWER: 32 teeth
3
14. Xander ran a total of 5 kilometers last month. How many kilometers did he run?
SOLUTION: So, Xander ran 125 kilometers.
ANSWER: 125 km
Write each expression using a positive exponent.
–4
15. 9
SOLUTION: –4
9
=
ANSWER: –2
16. (–10)
SOLUTION: –2
(–10)
=
ANSWER: –5
17. m
SOLUTION: –5
m
=
ANSWER: eSolutions Manual - Powered by Cognero
18. c
–5
Page 4
ANSWER: Chapter Review
–5
17. m
SOLUTION: –5
m
=
ANSWER: 18. c
–5
SOLUTION: c
–5
=
ANSWER: –3
19. (–4)
SOLUTION: –3
(–4)
=
ANSWER: 20. y
–9
SOLUTION: y
–9
=
ANSWER: Write each fraction as an expression using a negative exponent other than –1.
21. SOLUTION: –3
=6
ANSWER: –3
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eSolutions
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ANSWER: Chapter Review
Write each fraction as an expression using a negative exponent other than –1.
21. SOLUTION: –3
=6
ANSWER: –3
6
22. SOLUTION: or or
ANSWER: –6
2
–3
,4
–2
, or 8
23. SOLUTION: ANSWER: –3
5
24. SOLUTION: ANSWER: –5
3
25. SOLUTION: eSolutions Manualor
- Powered by Cognero
Page 6
ANSWER: Chapter
Review
–5
3
25. SOLUTION: or
ANSWER: –2
4
–4
or 2
26. SOLUTION: ANSWER: –3
3
27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.
SOLUTION: ANSWER: –3
10
Find each product or quotient. Express using exponents.
5
–2
28. 3 • 3
SOLUTION: ANSWER: 3
3
4
29. (–7) • (–7)
SOLUTION: eSolutions Manual - Powered by Cognero
Page 7
ANSWER: 3
3
Chapter
Review
4
29. (–7) • (–7)
SOLUTION: ANSWER: 5
(–7)
3
6
30. m • m
SOLUTION: ANSWER: 9
m
8
31. x • x
SOLUTION: ANSWER: x
9
7
32. (2h )(6h)
SOLUTION: ANSWER: 12h
8
–3
4
33. (5a )(–6a )
SOLUTION: ANSWER: –30a
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Page 8
ANSWER: Chapter
Review
8
12h
–3
4
33. (5a )(–6a )
SOLUTION: ANSWER: –30a
34. SOLUTION: ANSWER: –1
9
or
35. SOLUTION: ANSWER: k
6
8
9
36. Venus is about 10 kilometers from the Sun. Saturn is about 10 kilometers from the Sun. About how many times
farther from the Sun is Saturn than Venus?
SOLUTION: To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the
distance Venus is from the Sun.
So, Saturn is about 10 times further from the Sun than Venus.
ANSWER: about 10 times
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Express each number in standard form.
3
37. 5.82 × 10
Page 9
ANSWER: Chapter
Review
6
k
8
9
36. Venus is about 10 kilometers from the Sun. Saturn is about 10 kilometers from the Sun. About how many times
farther from the Sun is Saturn than Venus?
SOLUTION: To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the
distance Venus is from the Sun.
So, Saturn is about 10 times further from the Sun than Venus.
ANSWER: about 10 times
Express each number in standard form.
3
37. 5.82 × 10
SOLUTION: ANSWER: 5820
–2
38. 9.0 × 10
SOLUTION: ANSWER: 0.09
–4
39. 1.1 × 10
SOLUTION: ANSWER: 0.00011
40. 2.25 × 10
5
SOLUTION: ANSWER: 252,000
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Express each number in scientific notation.
41. 379
Page 10
ANSWER: Chapter
Review
0.00011
40. 2.25 × 10
5
SOLUTION: ANSWER: 252,000
Express each number in scientific notation.
41. 379
SOLUTION: ANSWER: 3.79 × 10
2
42. 0.000561
SOLUTION: ANSWER: 5.61 × 10
–4
43. 47,000
SOLUTION: ANSWER: 4
4.7 × 10
44. 0.0072
SOLUTION: ANSWER: –3
7.2 × 10
15
45. The mass of the Sun is 1.98892 × 10
exagrams. Express in standard form.
SOLUTION: eSolutions Manual - Powered by Cognero
So, the mass of the Sun is 1,988,920,000,000,000 exagrams.
Page 11
ANSWER: Chapter
–3Review
7.2 × 10
15
45. The mass of the Sun is 1.98892 × 10
exagrams. Express in standard form.
SOLUTION: So, the mass of the Sun is 1,988,920,000,000,000 exagrams.
ANSWER: 1,988,920,000,000,000 exagrams
Evaluate each expression. Express the result in scientific notation.
9
6
46. (4.45 × 10 )(1.3 × 10 )
SOLUTION: ANSWER: 5.785 × 10
15
47. SOLUTION: ANSWER: 11
1.5 × 10
4
5
48. (7.4 × 10 ) + (3.56 × 10 )
SOLUTION: ANSWER: eSolutions Manual5 - Powered by Cognero
4.39 × 10
7
5
49. (3.6 × 10 ) – (2.85 × 10 )
Page 12
ANSWER: Chapter
11Review
1.5 × 10
4
5
48. (7.4 × 10 ) + (3.56 × 10 )
SOLUTION: ANSWER: 4.39 × 10
5
7
5
49. (3.6 × 10 ) – (2.85 × 10 )
SOLUTION: ANSWER: 7
3.5715 × 10
4
5
50. A fin whale weighs 9.92 × 10 pounds. A blue whale weighs 2.87 × 10 pounds. Estimate how many more pounds
the blue whale weighs than the fin whale.
SOLUTION: 5
The blue whale weighs about 2 × 10 pounds more than the fin whale.
ANSWER: 5
about 2 × 10 pounds 4
3
51. A male elephant weighs 1.5 × 10 pounds. A female elephant weighs 7.9 × 10 pounds. How much more does the
male elephant weigh than the female elephant? Express your result in scientific notation.
SOLUTION: 3
The male elephant weights 7.1 × 10 pounds more than the female elephant.
ANSWER: 3 - Powered by Cognero
eSolutions Manual
7.1 × 10 lb
Find each square root or cube root.
Page 13
5
The blue whale weighs about 2 × 10 pounds more than the fin whale.
ANSWER: Chapter
Review
5
about 2 × 10 pounds 4
3
51. A male elephant weighs 1.5 × 10 pounds. A female elephant weighs 7.9 × 10 pounds. How much more does the
male elephant weigh than the female elephant? Express your result in scientific notation.
SOLUTION: 3
The male elephant weights 7.1 × 10 pounds more than the female elephant.
ANSWER: 3
7.1 × 10 lb
Find each square root or cube root.
52. SOLUTION: = 13
ANSWER: 13
53. SOLUTION: = –5
ANSWER: −5
54. SOLUTION: = –4
ANSWER: –4
55. SOLUTION: =9
ANSWER: 9
Estimate each square root or cube root to the nearest integer.
56. SOLUTION: eSolutions Manual - Powered by Cognero
The first perfect square less than 15 is 9.
Page 14
= 3
The first perfect square greater than 15 is 16.
= 4
SOLUTION: =9
ANSWER: Chapter
Review
9
Estimate each square root or cube root to the nearest integer.
56. SOLUTION: The first perfect square less than 15 is 9.
= 3
= 4
The first perfect square greater than 15 is 16.
The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,
is closer to 4 than to 3.
ANSWER: 4
57. SOLUTION: The first perfect square less than 52 is 49.
= 7
= 8
The first perfect square greater than 52 is 64.
The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,
to –7 than to –8.
is closer
ANSWER: −7
58. SOLUTION: The first perfect cube less than 90 is 64.
The first perfect cube greater than 90 is 125.
= 4
= 5
The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,
5.
is closer to 4 than to ANSWER: 4
59. SOLUTION: The first perfect cube less than 415 is 343.
The first perfect cube greater than 415 is 512.
= 7
= 8
The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,
than to 8.
is closer to 7 ANSWER: 7
60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by
the formula , where 꿟is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the
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period.
SOLUTION: Page 15
The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,
than to 8.
is closer to 7 ANSWER: Chapter
Review
7
60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by
the formula , where 꿟is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the
period.
SOLUTION: To find the period, substitute 8 for 꿟
.
The period of the pendulum is 3.14 seconds.
ANSWER: 3.14 s
Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer,
rational, or irrational.
61. 18
SOLUTION: Since 18 =
, this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational
number.
ANSWER: natural, whole, integer, rational
62. SOLUTION: is written as a fraction, so it is a rational number.
ANSWER: rational
63. SOLUTION: cannot be written as a fraction, so it is an irrational number.
ANSWER: irrational
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64. Page 16
is written as a fraction, so it is a rational number.
ANSWER: Chapter
Review
rational
63. SOLUTION: cannot be written as a fraction, so it is an irrational number.
ANSWER: irrational
64. SOLUTION: Since
, this number is a rational number.
ANSWER: rational
Replace the Ο with <, >, or = to make a true statement.
65. Ο SOLUTION: = 6.2525…
= 6.2449…
is to the right of Since
,
> .
ANSWER: > 66. Ο SOLUTION: = –8.3666…
−8
= –8.2
is to the left of −8 ,
Since
< −8 .
ANSWER: < 67. Ο SOLUTION: −11 = –11.1111…
= –11.1355…
SinceManual
is to thebyright
of
−11 - Powered
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ANSWER: , −11
>
.
Page 17
is to the left of −8 ,
Since
< −8 .
ANSWER: Chapter
Review
< 67. Ο SOLUTION: −11 = –11.1111…
= –11.1355…
Since −11
is to the right of
, −11
>
< .
.
ANSWER: > 68. Ο SOLUTION: = 8.2462…
= 8.4444…
Since
is to the left of ,
ANSWER: < Solve each equation. Round to the nearest tenth, if necessary.
3
69. m = 512
SOLUTION: The solutions is 8.
ANSWER: 8
2
70. 4y = 5.76
SOLUTION: The solutions are 1.2 and –1.2.
ANSWER: 1.2, Manual
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eSolutions
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71. The formula A ≈ 3.14r can be used to determine the area of a circle, where A is the area and r is the distance from
The solutions is 8.
ANSWER: 8
Chapter Review
2
70. 4y = 5.76
SOLUTION: The solutions are 1.2 and –1.2.
ANSWER: 1.2, −1.2
2
71. The formula A ≈ 3.14r can be used to determine the area of a circle, where A is the area and r is the distance from
the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the
distance from the center of the garden to the outside edge? Round to the nearest tenth.
SOLUTION: To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.
2
Substitute 700 for A in the equation A ≈ 3.14r .
Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.
ANSWER: 14.9 ft
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