## Elementary Algebra

Published by Cengage Learning

# Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Problem Set 11.3 - Page 489: 23

#### Answer

$\frac{1}{2}$

#### Work Step by Step

Whenever a number in the numerator of a fraction is raised to a negative power, we put the number in the denominator of the fraction and make the exponent positive. Therefore, $32^{-\frac{1}{5}}=\frac{1}{32^{\frac{1}{5}}}$ Now, recall the formula: $a^{\frac{b}{c}}=(\sqrt[c] a)^{b}$. Using this same formula, we obtain: $\frac{1}{32^{\frac{1}{5}}}=\frac{1}{(2^{5})^{\frac{1}{5}}}=\frac{1}{\sqrt[5] {2^{5}}}=\frac{1}{2}$

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