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: 28

Answer

$\frac{y^{5}}{3x^{3}}$

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, $\sqrt (\frac{y^{10}}{9x^{6}})=\frac{\sqrt (y^{10})}{\sqrt (9x^{6})}=\frac{y^{5}}{3x^{3}}$ We know that $\sqrt (y^{10})=y^{5}$, because $(y^{5})^{2}=y^{5\times2}=y^{10}$. Also, we know that $\sqrt (9x^{6})=3x^{3}$, because $(3x^{3})^{2}=(3\times3)\times x^{3+3}=9x^{6}$.
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