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Study Guide and Review
Write each expression using exponents.
11. 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
12. 4
SOLUTION: The base 4 is a factor 1 time. So, the exponent is 1.
1
4=4
13. x • x • x
SOLUTION: The base x is a factor 3 times. So the exponent is 3.
x • x • x = x
3
14. f • f • g • g • g • g
SOLUTION: Evaluate each expression.
15. 35
SOLUTION: 16. 2 • 43
SOLUTION: Evaluate each expression if w =
, x = 4, y = 1, and z = –5.
17. x2 – 6
SOLUTION: 18. w3 + y 2
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18. w3 + y 2
SOLUTION: 19. 2(y + z 3)
SOLUTION: 20. w4x2yz
SOLUTION: 21. TEETH Adult humans have 25 teeth. How many teeth do adults have?
SOLUTION: So, adult humans have 32 teeth.
Write the prime factorization of each number. Use exponents for repeated factors.
22. 34
SOLUTION: 34 = 2 • 17
23. 40
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24. 63
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Write the prime factorization of each number. Use exponents for repeated factors.
22. 34
SOLUTION: Study
34 =Guide
2 • 17 and Review
23. 40
SOLUTION: 24. 63
SOLUTION: 25. 225
SOLUTION: Factor each monomial.
26. 18x
SOLUTION: 18x = 2 • 3 • 3 • x
27. 10r2
SOLUTION: 28. 32pq
SOLUTION: 32pq = 2 • 2 • 2 • 2 • 2 • p • q
29. –25ab2
SOLUTION: 30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers
of rows and columns can she display them if each row has the same number of photographs? Name each
arrangement.
SOLUTION: List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the
• 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 differentPage 3
arrangements.
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29. –25ab
SOLUTION: Study Guide and Review
30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers
of rows and columns can she display them if each row has the same number of photographs? Name each
arrangement.
SOLUTION: List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the
following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different
arrangements.
Find each product or quotient. Express using exponents.
31. 35 • 32
SOLUTION: 32. (–7) • (–7)4
SOLUTION: 33. m3 • m6
SOLUTION: 34. x8 • x
SOLUTION: 35. (2h 7)(6h)
SOLUTION: 36. (5a 3)(–6a 4)
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36. (5a 3)(–6a 4)
SOLUTION: 37. SOLUTION: 38. SOLUTION: 39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 109 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.
Write each expression using a positive exponent.
40. 9–4
SOLUTION: –4
9
=
41. (–10)–2
SOLUTION: –2
(–10)
=
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42. m–5
SOLUTION: Page 5
SOLUTION: –4
9 Guide
=
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41. (–10)–2
SOLUTION: –2
(–10)
=
42. m–5
SOLUTION: –5
m
=
Write each fraction as an expression using a negative exponent other than –1.
43. SOLUTION: –3
=6
44. SOLUTION: or or
45. SOLUTION: 46. MEASUREMENT If 1 millimeter is equal to 10–3 meter and 1 nanometer is equal to 10–9 meter, how many
nanometers are in 1 millimeter? Write using a positive exponent.
SOLUTION: To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of
nanometers in a meter.
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So, there are 10 nanometers in 1 millimeter.
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46. MEASUREMENT If 1 millimeter is equal to 10–3 meter and 1 nanometer is equal to 10–9 meter, how many
nanometers are in 1 millimeter? Write using a positive exponent.
SOLUTION: To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of
nanometers in a meter.
6
So, there are 10 nanometers in 1 millimeter.
Express each number in standard form.
47. 5.82 × 103
SOLUTION: 48. 9.0 × 10–2
SOLUTION: 49. 3.4 × 10–4
SOLUTION: 50. 1.705 × 105
SOLUTION: Express each number in scientific notation.
51. 379
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52. 26,880
SOLUTION: Page 7
50. 1.705 × 10
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Express each number in scientific notation.
51. 379
SOLUTION: 52. 26,880
SOLUTION: 53. 0.0014
SOLUTION: 54. 0.000561
SOLUTION: 55. SPACE The mass of the Sun is 1.98892 × 1015 exagrams. Express in standard form.
SOLUTION: So, the mass of the Sun is 1,988,920,000,000,000 exagrams.
Simplify.
56. (26)3
SOLUTION: 57. (r2)8
SOLUTION: 58. (3x7)2
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58. (3x7)2
SOLUTION: 59. (–2n 4)6
SOLUTION: 60. (4a 9b)4
SOLUTION: 61. (5w5x8)3
SOLUTION: 62. GEOMETRY Find the area of the square shown below.
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