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: 73

Answer

$\dfrac{\sqrt[4]{96a^{10}b^{3}}}{\sqrt[4]{3a^{2}b^{3}}}=2a^{2}\sqrt[4]{2}$

Work Step by Step

$\dfrac{\sqrt[4]{96a^{10}b^{3}}}{\sqrt[4]{3a^{2}b^{3}}}$ Rewrite the expression as $\sqrt[4]{\dfrac{96a^{10}b^{3}}{3a^{2}b^{3}}}$ and evaluate the division inside the root: $\dfrac{\sqrt[4]{96a^{10}b^{3}}}{\sqrt[4]{3a^{2}b^{3}}}=\sqrt[4]{\dfrac{96a^{10}b^{3}}{3a^{2}b^{3}}}=\sqrt[4]{32a^{10-2}}=\sqrt[4]{32a^{8}}=...$ Rewrite the expression inside the root as $16\cdot2\cdot a^{8}$ and simplify: $...=\sqrt[4]{16\cdot2\cdot a^{8}}=2a^{2}\sqrt[4]{2}$
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