Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 30

Answer

$\dfrac{9y}{\sqrt[4]{4y^{9}}}=\dfrac{9\sqrt[4]{4y^{3}}}{2y^{2}}$

Work Step by Step

$\dfrac{9y}{\sqrt[4]{4y^{9}}}$ Simplify the expression: $\dfrac{9y}{\sqrt[4]{4y^{9}}}=\dfrac{9y}{y^{2}\sqrt[4]{4y}}=\dfrac{9}{y\sqrt[4]{4y}}=...$ Multiply the fraction by $\dfrac{\sqrt[4]{4y^{3}}}{\sqrt[4]{4y^{3}}}$ and simplify: $...=\dfrac{9}{y\sqrt[4]{4y}}\cdot\dfrac{\sqrt[4]{4y^{3}}}{\sqrt[4]{4y^{3}}}=\dfrac{9\sqrt[4]{4y^{3}}}{y\sqrt[4]{16y^{4}}}=\dfrac{9\sqrt[4]{4y^{3}}}{y(2y)}=\dfrac{9\sqrt[4]{4y^{3}}}{2y^{2}}$
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