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: 75

Answer

$\dfrac{\sqrt[5]{64x^{10}y^{3}}}{\sqrt[5]{2x^{3}y^{-7}}}=2xy^{2}\sqrt[5]{x^{2}}$

Work Step by Step

$\dfrac{\sqrt[5]{64x^{10}y^{3}}}{\sqrt[5]{2x^{3}y^{-7}}}$ Rewrite this expression as $\sqrt[5]{\dfrac{64x^{10}y^{3}}{2x^{3}y^{-7}}}$ and evaluate the division inside the root: $\dfrac{\sqrt[5]{64x^{10}y^{3}}}{\sqrt[5]{2x^{3}y^{-7}}}=\sqrt[5]{\dfrac{64x^{10}y^{3}}{2x^{3}y^{-7}}}=\sqrt[5]{32x^{10-3}y^{3+7}}=\sqrt[5]{32x^{7}y^{10}}=...$ Simplify: $...=2xy^{2}\sqrt[5]{x^{2}}$
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