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: 29

Answer

$\dfrac{5a}{\sqrt[5]{8a^{9}b^{11}}}=\dfrac{5\sqrt[5]{4ab^{4}}}{2ab^{3}}$

Work Step by Step

$\dfrac{5a}{\sqrt[5]{8a^{9}b^{11}}}$ Simplify the expression: $\dfrac{5a}{\sqrt[5]{8a^{9}b^{11}}}=\dfrac{5a}{ab^{2}\sqrt[5]{8a^{4}b}}=\dfrac{5}{b^{2}\sqrt[5]{8a^{4}b}}=...$ Multiply the fraction by $\dfrac{\sqrt[5]{4ab^{4}}}{\sqrt[5]{4ab^{4}}}$ and simplify: $...=\dfrac{5}{b^{2}\sqrt[5]{8a^{4}b}}\cdot\dfrac{\sqrt[5]{4ab^{4}}}{\sqrt[5]{4ab^{4}}}=\dfrac{5\sqrt[5]{4ab^{4}}}{b^{2}\sqrt[5]{32a^{5}b^{5}}}=\dfrac{5\sqrt[5]{4ab^{4}}}{b^{2}(2ab)}=\dfrac{5\sqrt[5]{4ab^{4}}}{2ab^{3}}$
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