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 (7^{2})^{4} = 7^{2 Â· 4}
= 7^{8}
Example
a. Use the Power of a Power Property of Exponents to simplify (5^{2})^{3}.
b. Use the definition of exponential notation to justify your answer.
Solution
a. To raise a power to a power, multiply the exponents.
(5^{2})^{3} = 5^{2 Â· 3}
= 5^{6}
b. Rewrite each power to show the factors. Then simplify.
Example 2
Simplify: (y^{5})^{3 }
Solution
To simplify a power of a power,
multiply the exponents. (y^{5})^{3} = y^{5
Â· 3} = y^{15}
