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 - Test: Chapter 10 - Page 695: 10



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 given expression is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{4w}\sqrt{4v^2} \\\\= \sqrt[3]{4w(4v^2)} \\\\= \sqrt[3]{16wv^2} .\end{array} Extracting the factors that are perfect powers of the index, the expression above simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{16wv^2} \\\\= \sqrt[3]{8\cdot2wv^2} \\\\= \sqrt[3]{(2)^3\cdot2wv^2} \\\\= 2\sqrt[3]{2wv^2} .\end{array}
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