The following suggests a rule for multiplying powers with the same base.

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The following suggests a rule for multiplying
powers with the same base.
24 22 (2 2 2 2) (2 2) 26
a3 a2 (a a a) (a a) a5
Notice that the sum of the exponents in each
expression equals the exponent in the answer 4
2 6 and 3 2 5.
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Additional Example 1 Multiplying Powers with the
Same Base
Simplify each expression. Write your answer in
exponential form.
Add exponents.
B. n5 n7
Add exponents.
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Check It Out! Example 1
Simplify each expression. Write your answer in
exponential form.
Add exponents.
B. x2 x3
Add 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 each expression. Write your answer in
exponential form.
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 each expression. Write your answer in
exponential form.
D. (172)20
C.
Multiply exponents.
172 20
1740
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Check It Out! Example 3
Simplify each expression. Write your answer in
exponential form.
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 each expression. Write your answer in
exponential form.
D. (134)10
C.
Multiply exponents.
134 10
1340