Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 22

Answer

$\frac{\sqrt[4] (a^{3})}{3}$

Work Step by Step

The quotient rule holds that $\sqrt[n] (\frac{a}{b})=\frac{\sqrt[n] a}{\sqrt[n] b}$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero). Therefore, $\sqrt[4] (\frac{a^{3}}{81})=\frac{\sqrt[4] (a^{3})}{\sqrt[4] 81}=\frac{\sqrt[4] (a^{3})}{3}$ We know that $\sqrt[4] 81=3$, because $3^{4}=81$.
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