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: 28

Answer

$\sqrt[5]{\dfrac{32}{m^{6}n^{13}}}=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{m^{2}n^{3}}$

Work Step by Step

$\sqrt[5]{\dfrac{32}{m^{6}n^{13}}}$ Rewrite this expression as $\dfrac{\sqrt[5]{32}}{\sqrt[5]{m^{6}n^{13}}}$ and simplify it: $\sqrt[5]{\dfrac{32}{m^{6}n^{13}}}=\dfrac{\sqrt[5]{32}}{\sqrt[5]{m^{6}n^{13}}}=\dfrac{2}{mn^{2}\sqrt[5]{mn^{3}}}=...$ Multiply the fraction by $\dfrac{\sqrt[5]{m^{4}n^{2}}}{\sqrt[5]{m^{4}n^{2}}}$ and simplify: $...=\dfrac{2}{mn^{2}\sqrt[5]{mn^{3}}}\cdot\dfrac{\sqrt[5]{m^{4}n^{2}}}{\sqrt[5]{m^{4}n^{2}}}=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{mn^{2}\sqrt[5]{m^{5}n^{5}}}=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{mn^{2}(m)(n)}=...$ $...=\dfrac{2\sqrt[5]{m^{4}n^{2}}}{m^{2}n^{3}}$
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