## College Algebra (6th Edition)

Published by Pearson

# Chapter P - Summary, Review, and Test - Review Exercises: 57

#### Answer

Not a real number

#### Work Step by Step

Based on the definition of $a^{\frac{m}{n}}$, we know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}=\sqrt[n] a^{m}$ (where $\sqrt[n] a$ is a real number). Therefore, $\sqrt[4] (-5)^{4}=(\sqrt[4] -5)^{4}$. We know that this cannot be a real number, as $\sqrt[4] -5$ is not real number, because there is no number $a$ such that $a^{4}=-5$.

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