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 - Mid-Chapter Review - Mixed Review - Page 663: 25



Work Step by Step

Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel} \sqrt[3]{12x^2y^5}\sqrt[3]{18x^7y} \\\\= \sqrt[3]{12x^2y^5(18x^7y)} \\\\= \sqrt[3]{(2\cdot2\cdot3)x^{2+7}y^{5+1}(2\cdot3\cdot3)} \\\\= \sqrt[3]{2^33^3x^{9}y^{6}} .\end{array} Extracting the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{2^33^3x^{9}y^{6}} \\\\= \sqrt[3]{(2\cdot3x^{3}y^{2})^3} \\\\= 2\cdot3x^{3}y^{2} \\\\= 6x^{3}y^{2} .\end{array}
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