Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Review: 94

Answer

$-4ab\sqrt[4]{2b}$

Work Step by Step

Using the properties of radicals, the expression $ 2a\sqrt[4]{32b^5}-3b\sqrt[4]{162a^4b}+\sqrt[4]{2a^4b^5} $ simplifies to \begin{array}{l} 2a\sqrt[4]{16b^4\cdot2b}-3b\sqrt[4]{81a^4\cdot2b}+\sqrt[4]{a^4b^4\cdot2b} \\= 2a\cdot2b\sqrt[4]{2b}-3b\cdot3a\sqrt[4]{2b}+ab\sqrt[4]{2b} \\= 4ab\sqrt[4]{2b}-9ab\sqrt[4]{2b}+ab\sqrt[4]{2b} \\= -4ab\sqrt[4]{2b} .\end{array}
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