College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding: 47

Answer

$(-x-5y)\sqrt[3]{2xy}=-(x+5y)\sqrt[3]{2xy}$

Work Step by Step

We simplify: $\sqrt[3]{16x^4y}-3x\sqrt[3]{2xy}+5\sqrt[3]{-2xy^4}=\sqrt[3]{8*2x^3xy}-3x\sqrt[3]{2xy}+5\sqrt[3]{-1*2xy^3y}=2x\sqrt[3]{2xy}-3x\sqrt[3]{2xy}-5y\sqrt[3]{2xy}=(2x-3x-5y)\sqrt[3]{2xy}=(-x-5y)\sqrt[3]{2xy}=-(x+5y)\sqrt[3]{2xy}$
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