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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 (x^m)ⁿ = x^mn (Here, m and n are positive integers.)

Example (7²)⁴ = 7^{2 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 = 5^{2 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 = y^{5
Â· 3} = y¹⁵