9-3 Multiplying and Dividing Monomials
Find each product. Express using exponents.
10. 56 ∙ 52
SOLUTION: 11. (–2)3 ∙ (–2)2
SOLUTION: 12. a 7 ∙ a 2
SOLUTION: 13. (t3)(t3)
SOLUTION: 14. (10x)(4x7)
SOLUTION: 15. 6p 7 ∙ 9p 7
SOLUTION: 16. m5 ∙ (–4m6)
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9-3 Multiplying and Dividing Monomials
16. m5 ∙ (–4m6)
SOLUTION: 17. (–8s3)(–3s4)
SOLUTION: Find each quotient. Express using exponents.
18. SOLUTION: 19. SOLUTION: 20. SOLUTION: 21. SOLUTION: eSolutions
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SOLUTION: 9-3 Multiplying and Dividing Monomials
21. SOLUTION: 22. (–1.5)8 ÷ (–1.5)3
SOLUTION: 23. 815 ÷ 89
SOLUTION: 24. r20 ÷ r6
SOLUTION: 25. (–n)6 ÷ (–n)4
SOLUTION: 26. SOUND Sound intensity is measured in decibels. The decibel scale is based on powers of ten as shown.
a. How many times as intense is a rock concert as normal conversation?
b. How many times as intense is a vacuum cleaner as a person whispering?
SOLUTION: a. Divide the intensity of a rock concert by the intensity of a normal conversation.
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A rock concert is 10 or 100,000 times as intense as a normal conversation.
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SOLUTION: 9-3 Multiplying and Dividing Monomials
26. SOUND Sound intensity is measured in decibels. The decibel scale is based on powers of ten as shown.
a. How many times as intense is a rock concert as normal conversation?
b. How many times as intense is a vacuum cleaner as a person whispering?
SOLUTION: a. Divide the intensity of a rock concert by the intensity of a normal conversation.
5
A rock concert is 10 or 100,000 times as intense as a normal conversation.
b. Divide the intensity of a vacuum cleaner by the intensity of a person whispering.
6
A vacuum cleaner is 10 or 1,000,000 times as intense as a person whispering.
27. RUNNING A person weighing 53 pounds can experience forces 5 times their body weight while running. Find 53 ∙
5 to find the number of pounds exerted on a person’s foot while running.
SOLUTION: 4
5 or 625 pounds are exerted on a person’s foot while running.
28. SEA CUCUMBERS The largest sea cucumbers are more than 102 times longer than the smallest sea cucumbers.
If the smallest species of sea cucumbers are about 10 millimeters long, find the approximate length of the largest sea
cucumbers.
SOLUTION: 3
The approximate length of the largest sea cucumbers is 10 or 1000 millimeters.
29. HEALTH A nurse draws a sample of blood. A cubic millimeter of the blood contains 225 red blood cells and 223
white blood cells. Compare the number of red blood cells to the number of white blood cells as a fraction. Explain its
meaning.
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SOLUTION: Page 4
9-3 Multiplying and Dividing Monomials
3
The approximate length of the largest sea cucumbers is 10 or 1000 millimeters.
29. HEALTH A nurse draws a sample of blood. A cubic millimeter of the blood contains 225 red blood cells and 223
white blood cells. Compare the number of red blood cells to the number of white blood cells as a fraction. Explain its
meaning.
SOLUTION: The fraction of the number red blood cells to white blood cells is
. For every 484 red blood cells, there is one
white blood cell.
Find each missing exponent.
30. SOLUTION: 1
2
3
When multiplying powers, the exponents are added. 1 + 2 = 3, so (5 )(5 ) = 5 . The missing exponent is 1.
31. SOLUTION: 10
5
15
12
7
19
When multiplying powers, the exponents are added. 10 + 5 = 15, so (9 )(9 ) = 9 . The missing exponent is 5.
32. SOLUTION: When multiplying powers, the exponents are added. 12 + 7 = 19, so (a )(a ) = a . The missing exponent is 7.
33. SOLUTION: When dividing powers, the exponents are subtracted. 12 − 4 = 8, so
. The missing exponent is 12.
34. SOLUTION: When dividing powers, the exponents are subtracted. 7 − 7 = 0, so
. The missing exponent is 7.
35. SOLUTION: 10
2
8
When dividing powers, the exponents are subtracted. 10 − 2 = 8, so c ÷ c = c . The missing exponent is 2.
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36. MULTIPLE REPRESENTATIONS In this problem, you will investigate area and volume. The formulas A = s2
3
and V = s can be used to find the area of a square and the volume of a cube, respectively, with side length s.
SOLUTION: 9-3 When
Multiplying
and Dividing
Monomials
dividing powers,
the exponents
are subtracted. 7 − 7 = 0, so
. The missing exponent is 7.
35. SOLUTION: 10
2
8
When dividing powers, the exponents are subtracted. 10 − 2 = 8, so c ÷ c = c . The missing exponent is 2.
36. MULTIPLE REPRESENTATIONS In this problem, you will investigate area and volume. The formulas A = s2
3
and V = s can be used to find the area of a square and the volume of a cube, respectively, with side length s.
a. Tabular Copy and complete the table shown.
b. Verbal How are the area and volume each affected if the side length is doubled? tripled?
c. Verbal How are the area and volume each affected if the side length is squared? cubed?
SOLUTION: a.
Side
Length
(units)
s
Area of Square
(units2)
Volume of Cube (units3)
2
s
2s
(2s) = (2s)(2s)
2
= 4s
(2s) = (2s)(2s)(2s) = 8s
3s
(3s) = (3s)(3s)
2
= 9s
s
s
2
3
s
2
2
2 2
2
2
3 2
3
3
(s ) = (s )(s ) =
4
s
3
3
3
3
(3s) = (3s)(3s)(3s) = 27s
2 3
2
2
2
6
3 3
3
3
3
9
(s ) = (s )(s )(s ) = s
3
(s ) = (s )(s ) =
(s ) = (s )(s )(s ) = s
6
s
b. If the side length is doubled, the area is quadrupled and the volume is multiplied by 8. If the side length is tripled,
2
3
the area is multiplied by 3 or 9 and the volume is multiplied by 3 or 27.
c. If the side length is squared, the area and volume are squared. If the side length is cubed, the area and volume are
cubed.
Find each product or quotient. Express using exponents.
37. ab5 ∙ 8a2b 5
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b. If the side length is doubled, the area is quadrupled and the volume is multiplied by 8. If the side length is tripled,
2
3
9-3
the area is multiplied by 3 or 9 and the volume is multiplied by 3 or 27.
c.
If the side length
is squared,
the area
and volume are squared. If the side length is cubed, the area and volume are
Multiplying
and
Dividing
Monomials
cubed.
Find each product or quotient. Express using exponents.
37. ab5 ∙ 8a2b 5
SOLUTION: 38. 10x3y ∙ (–2xy2)
SOLUTION: 39. SOLUTION: 40. SOLUTION: eSolutions Manual - Powered by Cognero
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