Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - Chapter Test - Page 427: 10

Answer

$\dfrac{1}{25}$

Work Step by Step

We want to break down this problem a little to be able to work with it. The number $125$ can be broken down to a small base raised to a power: $5^3$. Let's rewrite the problem: $(5^3)^{-2/3}$ Raising a power to a power means we can multiply the two powers or exponents together: $5^{3(-2/3)}$ Multiply the exponents to simplify: $5^{-6/3}$ Reduce the fraction in the exponent by dividing both numerator and denominator by the greatest common factor, which is $3$, in this case: $5^{-2}$ Use the rule $a^{-m}=\dfrac{1}{a^m}$ to obtain: $\dfrac{1}{5^{2}}$ Let's evaluate $5^2$: $\dfrac{1}{25}$
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