Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Section 10.3 - Simplifying Radical Expressions - Exercise Set: 76

Answer

$\dfrac{\sqrt[5]{192x^{6}y^{12}}}{\sqrt[5]{2x^{-1}y^{-3}}}=2xy^{3}\sqrt[5]{3x^{2}}$

Work Step by Step

$\dfrac{\sqrt[5]{192x^{6}y^{12}}}{\sqrt[5]{2x^{-1}y^{-3}}}$ Rewrite this expression as $\sqrt[5]{\dfrac{192x^{6}y^{12}}{2x^{-1}y^{-3}}}$ and evaluate the division inside the root: $\dfrac{\sqrt[5]{192x^{6}y^{12}}}{\sqrt[5]{2x^{-1}y^{-3}}}=\sqrt[5]{\dfrac{192x^{6}y^{12}}{2x^{-1}y^{-3}}}=\sqrt[5]{96x^{6+1}y^{12+3}}=\sqrt[5]{96x^{7}y^{15}}=...$ Rewrite the expression inside the root as $32\cdot3\cdot x^{7}y^{15}$ and simplify: $...=\sqrt[5]{32\cdot3\cdot x^{7}y^{15}}=2xy^{3}\sqrt[5]{3x^{2}}$
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