## Intermediate Algebra (12th Edition)

$-7\sqrt[3]{ x^2y}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $3\sqrt[3]{x^2y}-5\sqrt[3]{8x^2y} ,$ 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]{x^2y}-5\sqrt[3]{8\cdot x^2y} \\\\= 3\sqrt[3]{x^2y}-5\sqrt[3]{(2)^3\cdot x^2y} .\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]{x^2y}-5(2)\sqrt[3]{ x^2y} \\\\= 3\sqrt[3]{x^2y}-10\sqrt[3]{ x^2y} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (3-10)\sqrt[3]{ x^2y} \\\\= -7\sqrt[3]{ x^2y} .\end{array}