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9-1 Powers and Exponents
Write each expression using exponents.
1. 2 • 2 • 2 • 2 • 2 • 2
SOLUTION: The base 2 is a factor 6 times. So, the exponent is 6.
6
2 • 2 • 2 • 2 • 2 • 2 = 2
2. d • d • d • d • d • d
SOLUTION: The base d is a factor 6 times. So, the exponent is 6.
6
d • d • d • d • d • d = d
3. SOLUTION: The base
is a factor 3 times. So, the exponent is 3.
4. 4 • m • m • m • q • q • q
SOLUTION: 5. (y – 3)(y – 3)(y – 3)
SOLUTION: The base (y – 3) is a factor 3 times. So, the exponent is 3.
3
(y – 3)(y – 3)(y – 3)= (y – 3)
6. (a + 1)(a + 1)
SOLUTION: The base (a + 1) is a factor 2 times. So, the exponent is 2.
2
(a + 1)(a + 1)= (a + 1)
7. INSECTS The longhorn beetle can have a body length of over 24 centimeters. How many centimeters long is this?
SOLUTION: The longhorn beetle can have a body length of over 16 cm.
8. E-MAIL Theo sends an e-mail to three friends. Each friend forwards the e-mail to three friends. Each of those
friends
forwards
it to
three friends,
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Then find the value of the power.
SOLUTION: and so on. Find the number of e-mails sent during the fifth stage as a power. Page 1
SOLUTION: 9-1 Powers and Exponents
The longhorn beetle can have a body length of over 16 cm.
8. E-MAIL Theo sends an e-mail to three friends. Each friend forwards the e-mail to three friends. Each of those
friends forwards it to three friends, and so on. Find the number of e-mails sent during the fifth stage as a power.
Then find the value of the power.
SOLUTION: The email is sent each time to 3 friends. So, the base is 3. During the 5th stage the exponent is 5.
5
So, the number of emails sent is 3 .
Evaluate each expression if a = 3, b = –4, and c = 3.5.
9. a 3 + 2
SOLUTION: 10. 3(b – 1)2
SOLUTION: 11. c2 + b 2
SOLUTION: Write each expression using exponents.
12. 11 • 11 • 11 • 11
SOLUTION: The base 11 is a factor 4 times. So, the exponent is 4.
4
11 • 11 • 11 • 11 = 11
13. 3 • 3 • 3 • 3 • 3
SOLUTION: The base 3 is a factor 5 times. So, the exponent is 5.
5
3 • 3 • 3 • 3 • 3 = 3
14. (–8)(–8)(–8)(–8)(–8)(–8)
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The base (–8) is a factor 6 times. So, the exponent is 6.
6
(–8)(–8)(–8)(–8)(–8)(–8) = (–8)
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13. 3 • 3 • 3 • 3 • 3
SOLUTION: The base 3 is a factor 5 times. So, the exponent is 5.
9-1 Powers and Exponents
5
3 • 3 • 3 • 3 • 3 = 3
14. (–8)(–8)(–8)(–8)(–8)(–8)
SOLUTION: The base (–8) is a factor 6 times. So, the exponent is 6.
6
(–8)(–8)(–8)(–8)(–8)(–8) = (–8)
15. (–14) • (–14) • (–14)
SOLUTION: The base (–14) is a factor 3 times. So, the exponent is 3.
3
(–14) • (–14) • (–14) = (–14)
16. SOLUTION: The base
is a factor 4 times. So, the exponent is 4.
17. (–1.5)(–1.5)(–1.5)
SOLUTION: The base (–1.5) is a factor 3 times. So, the exponent is 3.
3
(–1.5)(–1.5)(–1.5)= (–1.5)
18. ab • ab • ab • ab
SOLUTION: The base ab is a factor 4 times. So, the exponent is 4.
ab • ab • ab • ab =(ab)
4
19. 5 • p • p • p • q • q • q
SOLUTION: 20. 3 • 7 • m • m • n • n • n • n
SOLUTION: 21. 8(c + 4)(c + 4)
SOLUTION: The base (c + 4) is a factor 2 times. So, the exponent is 2.
2
8(c + 4)(c + 4)= 8(c + 4)
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22. (n – 5)(n – 5)(n – 5)
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20. 3 • 7 • m • m • n • n • n • n
SOLUTION: 9-1 Powers and Exponents
21. 8(c + 4)(c + 4)
SOLUTION: The base (c + 4) is a factor 2 times. So, the exponent is 2.
2
8(c + 4)(c + 4)= 8(c + 4)
22. (n – 5)(n – 5)(n – 5)
SOLUTION: The base (n – 5) is a factor 3 times. So, the exponent is 3.
3
(n – 5)(n – 5)(n – 5)= (n – 5)
23. (2x + 3y)(2x + 3y)
SOLUTION: The base (2x + 3y) is a factor 2 times. So, the exponent is 2.
2
(2x + 3y)(2x + 3y)= (2x + 3y)
24. VOLCANOES The longest chain of active volcanoes is in the South Pacific. This chain is more than 3 • 104 miles
5
long and has approximately 3 • 5 volcanoes.
a. How long is the chain of volcanoes?
b. How many volcanoes are there?
SOLUTION: a.
The chain of volcanoes is 30,000 miles long.
b.
There are 1215 volcanoes.
Evaluate each expression if x = –2, y = 3, and z = 2.5.
25. y 4
SOLUTION: 26. z 3
SOLUTION: 2
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SOLUTION: Page 4
26. z
SOLUTION: 9-1 Powers and Exponents
27. 7x2
SOLUTION: 28. xy3
SOLUTION: 29. z 2 + x
SOLUTION: 30. y 0 + 9
SOLUTION: 31. 2y + z 3
SOLUTION: 32. x2 + 2y – 3
SOLUTION: 33. y 2 – 3x + 8
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9-1 Powers and Exponents
33. y 2 – 3x + 8
SOLUTION: 34. 4(y + 1)4
SOLUTION: 35. 3(2z + 4)2
SOLUTION: 36. 5(x3 + 6)
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