Learn to apply the properties of exponents.

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Learn to apply the properties of exponents.
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The factors of a power, such as 74, can be
grouped in different ways. Notice the
relationship of the exponents in each product.
7 7 7 7 74
(7 7 7) 7 73 71 74
(7 7) (7 7) 72 72 74
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Additional Example 1 Multiplying Powers with the
Same Base
Multiply. Write the product as one power.
Add exponents.
B. n5 n7
Add exponents.
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Additional Example 1 Multiplying Powers with the
Same Base Continued
Multiply. Write the product as one power.
C. 25 2
Add exponents.
D. 244 244
Add exponents.
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Check It Out Example 1
Multiply. Write the product as one power.
Add exponents.
B. x2 x3
Add exponents.
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Check It Out Example 1
Multiply. Write the product as one power.
C. x5 y2
Cannot combine the bases are not the same.
x5 y2
D. 412 417
Add exponents.
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Notice what occurs when you divide powers with
the same base.
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Additional Example 2 Dividing Powers with the
Same Base
Divide. Write the quotient as one power.
A.
Subtract exponents.
B.
Subtract exponents.
x
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Check It Out Example 2
Divide. Write the product as one power.
9
9
A.
9
2
Subtract exponents.
97
e
10
B.
e
5
Subtract exponents.
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RAISING A POWER TO A POWER
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Additional Example 3 Raising a Power to a Power
Simplify.
A. (54)2
(54)2
Multiply exponents.
54 2
58
B. (67)9
(67)9
Multiply exponents.
67 9
663
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Additional Example 3 Raising a Power to a Power
Simplify.
D. (172) 20
C.
(172) 20
Multiply exponents.
Multiply exponents.
172 20
1740
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Check It Out Example 3
Simplify.
A. (33)4
(33)4
Multiply exponents.
33 4
312
B. (48)2
(48)2
Multiply exponents.
48 2
416
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Check It Out Example 3
Simplify.
D. (134) 10
C.
(134) 10
Multiply exponents.
Multiply exponents.
134 10
1340