Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Integrated Review - Radicals and Rational Exponents: 30

Answer

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

Work Step by Step

$\sqrt[3] {54y^{4}}-y\sqrt[3] {16y}$ =$\sqrt[3] {2\times27\times y^{3}\times y}-y\sqrt[3] {8\times2y}$ =$(\sqrt[3] 2\times \sqrt[3] {27}\times \sqrt[3] {y^{3}}\times \sqrt[3] y)-y(\sqrt[3] 8\times\sqrt[3] {2y})$ =$(\sqrt[3] 2\times \sqrt[3] {3^{3}}\times \sqrt[3] {y^{3}}\times \sqrt[3] y)-y(\sqrt[3] {2^{3}}\times\sqrt[3] {2y})$ =$(\sqrt[3] 2\times 3\times y\times \sqrt[3] y)-y(2\times\sqrt[3] {2y})$ =$(3y\sqrt[3] {2y})-(2y\sqrt[3] {2y})$ =$(3y-2y)\sqrt[3] {2y}$ =$y\sqrt[3] {2y}$
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