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: 74

Answer

$\dfrac{\sqrt[4]{160x^{10}y^{5}}}{\sqrt[4]{2x^{2}y^{2}}}=2x^{2}\sqrt[4]{5y^{3}}$

Work Step by Step

$\dfrac{\sqrt[4]{160x^{10}y^{5}}}{\sqrt[4]{2x^{2}y^{2}}}$ Rewrite this expression as $\sqrt[4]{\dfrac{160x^{10}y^{5}}{2x^{2}y^{2}}}$ and evaluate the division inside the root: $\dfrac{\sqrt[4]{160x^{10}y^{5}}}{\sqrt[4]{2x^{2}y^{2}}}=\sqrt[4]{\dfrac{160x^{10}y^{5}}{2x^{2}y^{2}}}=\sqrt[4]{80x^{10-2}y^{5-2}}=\sqrt[4]{80x^{8}y^{3}}=...$ Rewrite the expression inside the root as $16\cdot5\cdot x^{8}\cdot y^{3}$ and simplify: $...=\sqrt[4]{16\cdot5\cdot x^{8}\cdot y^{3}}=2x^{2}\sqrt[4]{5y^{3}}$
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