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# Power of a Power Property of Exponents

Property â€” Power of a Power Property of Exponents

English To raise a power to a power, multiply the exponents.

Algebra (xm)n = xmn (Here, m and n are positive integers.)

Example (72)4 = 72 Â· 4 = 78

Example

a. Use the Power of a Power Property of Exponents to simplify (52)3.

b. Use the definition of exponential notation to justify your answer.

Solution

a. To raise a power to a power,  multiply the exponents. (52)3 = 52 Â· 3 = 56

b. Rewrite each power to show the factors. Then simplify. Example 2

Simplify: (y5)3

Solution

To simplify a power of a power, multiply the exponents. (y5)3 = y5 Â· 3 = y15