Intermediate Algebra (6th Edition)

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

Chapter 7 - Sections 7.1-7.5 - Integrated Review - Radicals and Rational Exponents - Page 447: 30

Answer

$y\sqrt[3]{2y}$

Work Step by Step

Extracting the factors that are perfect powers of the index of the radical, the given expression, $ \sqrt[3]{54y^4}-y\sqrt[3]{16y} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{27y^3\cdot2y}-y\sqrt[3]{8\cdot2y} \\\\= \sqrt[3]{(3y)^3\cdot2y}-y\sqrt[3]{(2)^3\cdot2y} \\\\= 3y\sqrt[3]{2y}-y(2)\sqrt[3]{2y} \\\\= 3y\sqrt[3]{2y}-2y\sqrt[3]{2y} .\end{array} By combining like terms, the expression above becomes \begin{array}{l}\require{cancel} (3y-2y)\sqrt[3]{2y} \\\\= y\sqrt[3]{2y} .\end{array}
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