Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 38

Answer

$-\frac{6}{5}$

Work Step by Step

The quotient rule for radicals tells us that $\sqrt[n] \frac{a}{b}=\frac{\sqrt[n] a}{\sqrt[n] b}$ (if $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots. Therefore, $\sqrt[3] \frac{-216}{125}=\frac{\sqrt[3] (-216)}{\sqrt[3] 125}=\frac{-6}{5}=-\frac{6}{5}$. $\sqrt[3] -216=-6$, because $(-6)^{3}=-216$ $\sqrt[3] 125=5$, because $5^{3}=125$
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