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 - Page 432: 18


$\frac{\sqrt[4] y}{3x}$

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, $\sqrt[4] (\frac{y}{81x^{4}})=\frac{\sqrt[4] y}{\sqrt[4] (81x^{4})}=\frac{\sqrt[4] y}{3x}$ We know that $\sqrt[4] (81x^{4})=3x$, because $(3x)^{4}=(3\times3\times3\times3)\times x^{1+1+1+1}=81x^{4}$
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