Intermediate Algebra (6th Edition)

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

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set - Page 433: 72



Work Step by Step

Using the properties of radicals, then, \begin{array}{l} \dfrac{\sqrt[]{270y^2}}{5\sqrt[]{3y^{-4}}} \\\\= \dfrac{1}{5}\sqrt[]{\dfrac{270y^2}{3y^{-4}}} \\\\= \dfrac{1}{5}\sqrt[]{90y^{2-(-4)}} \\\\= \dfrac{1}{5}\sqrt[]{90y^{6}} \\\\= \dfrac{1}{5}\sqrt[]{9y^{6}\cdot10} \\\\= \dfrac{1}{5}\cdot3y^3\sqrt[]{10} \\\\= \dfrac{3y^3\sqrt[]{10}}{5} .\end{array}
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