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: 24

Answer

$\frac{\sqrt[3] 3}{2x^{2}}$

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, $\sqrt[3] (\frac{3}{8x^{6}})=\frac{\sqrt[3] 3}{\sqrt[3] (8x^{6})}=\frac{\sqrt[3] 3}{2x^{2}}$ We know that $\sqrt[3] (8x^{6})=2x^{2}$, because $(2x^{2})^{3}=(2\times2\times2)\times x^{2+2+2}=8x^{6}$.
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