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EXERCISES
A Practice by Example
For more practice, see Extra Practice.
Write each expression using a single exponent.
Example 1
(page 383)
1. A 3 3 B 7
Example 2
(page 384)
Algebra
5. A w-2 B -6
3. A h2 B 2
6. A -7 2 B 9
7. A p-2 B -1
Simplify each expression.
9. (3x)2
13. (abc)5
Example 3
(page 384)
2. A 9 2 B -5
10. A y ? y 2 B 5
14. A 10x 5 B 2
11. A 2x 2 B 4
15. A 10 5w B 2
Write each answer in scientific notation.
4. A y-3 B -4
8. A r 2 B 3
12. A a 2b 3 B 4
16. A y 2 ? 10 2 B 4
17. Geometry Find the area of a square whose side is 7.1 3 10 3 centimeters.
18. Geometry Find the area of a circle with a radius of 4 3 10-6 inches. Use
the formula A 5 pr2 and 3.14 for p.
B Apply Your Skills
Use R, S, or 5 to complete each statement.
19. 5 5 j A5 3 B 2
20. 8 2 ? 8 6 j A8 2 B 2
21. A5 3 B0 j 5 3 ? 5-3
25. 4 5 ? 4 6 j A4 5 B 6
26. (-3)4 j -3 4
27. (3 ? 4)7 j 12 7
22. A5 3 B 5 j 5 8
23. A 7-3 ? 7 5 B 3 j A7 2 B 6
24. 0 12 j 12 0
28. Computers A megabyte is 2 20 bytes. Use exponents to write 2 20 in four
different ways.
29. Writing in Math Explain how multiplying powers with the same base is
different from raising a power to a power.
30. Volcanoes A subdivision of the Kilauea Volcano in Hawaii erupted in
1967 and produced about 320,000 cubic meters of lava per day. Find the
total amount of lava produced if the eruption lasted about 8.3 months.
Assume there are 30 days in a month.
Write each expression using a single exponent.
31. A 2 1 ? 2 2 ? 2 3 B 2
34. A y ? y5 ? y10 B 2
32. A 3-2 ? 3-1 ? 30 B -3
35. A a ? 10-1 B 5
33. A A 5 2 B 3 B 2
36. A A m1 B 2 B 4
37. Error Analysis Beth thinks you can write x2 + x2 as 2x2. Clarissa thinks
you can write x2 + x2 as x4. Who is correct? Why?
38. Data File, p. 363 Write 2.3 megawatts in watts using standard form.
Simplify each expression.
39. A ab B c
40. A 3u2 B x
42. Reasoning Does (2 + 3)2 = 2 2 + 3 2? Explain.
41. A 5a ? 6b B x
7-4 Power Rules
385-386
C Challenge
43. A positive number is squared and the result is 25 16. Find the number,
and write it as a power.
44. Biology The diameter of a human eyebrow hair is 8.0 3 10-5 m.
Find the area of a cross section of an eyebrow hair. Use the formula
A = pr 2 and 3.14 for p.
45. Astronomy On January 1, 2004, Pluto will be about 2.9 3 10 9 miles
from Earth. Light travels about 1.86 3 10 5 miles per second. Find how
many hours it will take light to travel from Pluto to Earth.
46. Stretch Your Thinking Arrange these numbers from least to greatest:
4
2 222, A 2 22 B 2, (4) 4 , A 4 4 B 44
Test Prep
Multiple Choice
47. Find A 3.51 3 10-4 B 0.
A. 3.51 3 10-40 B. 0
C. 1
D. 3.51
48. The base of a crystal is a square with sides that measure
3 3 10-2 mm. Find the area of the base in square millimeters.
F. 3 3 10-4
G. 9 3 10-4
H. 9 3 10-2
I. 9 3 10-1
Take It to the NET
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Extended Response
49. Which number is equal to 0.0625?
A. 4 3 10-2
B. A 2-2 B 2
C. 6.25 3 10-1
50. Which number is greater than (35 3)7?
F. 35 10
G. 35 21
H. A 35 7 B 3
D. A 4-2 B -1
I. 35 37
51. A square has a side length of 7 3 10-3 m. Find the perimeter and the
area of the square. Write each answer in scientific notation. Explain
your work.
Mixed Review
Lesson 7-2
Algebra
Write each expression using a single exponent.
52. 15 20 ? 15 2
Lesson 6-9
53. z2 ? z12
54. m 10 ? m 20
Express each probability as a fraction and as a percent.
55. A letter chosen at random from the word V I D E O is a vowel.
56. An integer chosen at random from the numbers 1 to 10 is prime.
Lesson 6-1
Write each percent as a fraction in simplest form.
57. 20%
385-386
Chapter 7 Exponents and Powers
58. 33 13%
59. 1.75%