## Intermediate Algebra (12th Edition)

$(3-4x)\sqrt[3]{xy^2}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $3\sqrt[3]{xy^2}-2\sqrt[3]{8x^4y^2} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals. $\bf{\text{Solution Details:}}$ Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 3\sqrt[3]{xy^2}-2\sqrt[3]{8x^3\cdot xy^2} \\\\= 3\sqrt[3]{xy^2}-2\sqrt[3]{(2x)^3\cdot xy^2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 3\sqrt[3]{xy^2}-2(2x)\sqrt[3]{xy^2} \\\\= 3\sqrt[3]{xy^2}-4x\sqrt[3]{xy^2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (3-4x)\sqrt[3]{xy^2} .\end{array}