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: 26

Answer

$\dfrac{\sqrt[3]{3x}}{\sqrt[3]{4y^{4}}}=\dfrac{\sqrt[3]{6xy^{2}}}{2y^{2}}$

Work Step by Step

$\dfrac{\sqrt[3]{3x}}{\sqrt[3]{4y^{4}}}$ Simplify the denominator: $\dfrac{\sqrt[3]{3x}}{\sqrt[3]{4y^{4}}}=\dfrac{\sqrt[3]{3x}}{y\sqrt[3]{4y}}=...$ Multiply the fraction by $\dfrac{\sqrt[3]{2y^{2}}}{\sqrt[3]{2y^{2}}}$ and simplify the expression: $...=\dfrac{\sqrt[3]{3x}}{y\sqrt[3]{4y}}\cdot\dfrac{\sqrt[3]{2y^{2}}}{\sqrt[3]{2y^{2}}}=\dfrac{\sqrt[3]{6xy^{2}}}{y\sqrt[3]{8y^{3}}}=\dfrac{\sqrt[3]{6xy^{2}}}{y(2y)}=\dfrac{\sqrt[3]{6xy^{2}}}{2y^{2}}$
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