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: 27

Answer

$\sqrt[4]{\dfrac{16}{9x^{7}}}=\dfrac{2\sqrt[4]{9x}}{3x^{2}}$

Work Step by Step

$\sqrt[4]{\dfrac{16}{9x^{7}}}$ Rewrite this expression as $\dfrac{\sqrt[4]{16}}{\sqrt[4]{9x^{7}}}$ and simplify it: $\sqrt[4]{\dfrac{16}{9x^{7}}}=\dfrac{\sqrt[4]{16}}{\sqrt[4]{9x^{7}}}=\dfrac{2}{x\sqrt[4]{9x^{3}}}=...$ Multiply the fraction by $\dfrac{\sqrt[4]{9x}}{\sqrt[4]{9x}}$ and simplify: $...=\dfrac{2}{x\sqrt[4]{9x^{3}}}\cdot\dfrac{\sqrt[4]{9x}}{\sqrt[4]{9x}}=\dfrac{2\sqrt[4]{9x}}{x\sqrt[4]{81x^{4}}}=\dfrac{2\sqrt[4]{9x}}{x(3x)}=\dfrac{2\sqrt[4]{9x}}{3x^{2}}$
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