Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Review Exercises: Chapter 10: 29

Answer

$y\sqrt[3]{6}$

Work Step by Step

Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the given expression is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{60xy^3}}{\sqrt[3]{10x}} \\\\= \sqrt[3]{\dfrac{60xy^3}{10x}} \\\\= \sqrt[3]{\dfrac{\cancel{10}(6)\cancel{x}y^3}{\cancel{10}\cancel{x}}} \\\\= \sqrt[3]{6y^3} .\end{array} Extracting the factors that are perfect powers of the index, the expression above simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{6y^3} \\\\= \sqrt[3]{y^3\cdot 6} \\\\= \sqrt[3]{(y)^3\cdot 6} \\\\= y\sqrt[3]{6} .\end{array}
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