## Intermediate Algebra (12th Edition)

$12m\sqrt[3]{m}+15m\sqrt[4]{m}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $3\sqrt[3]{64m^4}+5\sqrt[4]{81m^5} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. $\bf{\text{Solution Details:}}$ 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]{64m^3\cdot m}+5\sqrt[4]{81m^4\cdot m} \\\\= 3\sqrt[3]{(4m)^3\cdot m}+5\sqrt[4]{(3m)^4\cdot m} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 3(4m)\sqrt[3]{m}+5(3m)\sqrt[4]{m} \\\\= 12m\sqrt[3]{m}+15m\sqrt[4]{m} .\end{array}