College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Summary, Review, and Test - Review Exercises: 65

Answer

5

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, $125^{\frac{1}{3}}=\sqrt[3] 125^{1}=\sqrt[3] 125=5$ We know that $\sqrt[3] 125=5$, because $5^{3}=125$.
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