## Intermediate Algebra (12th Edition)

$4x\sqrt[3]{x}+6x\sqrt[4]{x}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $2\sqrt[3]{8x^4}+3\sqrt[4]{16x^5} ,$ 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} 2\sqrt[3]{8x^3\cdot x}+3\sqrt[4]{16x^4\cdot x} \\\\= 2\sqrt[3]{(2x)^3\cdot x}+3\sqrt[4]{(2x)^4\cdot x} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2(2x)\sqrt[3]{x}+3(2x)\sqrt[4]{x} \\\\= 4x\sqrt[3]{x}+6x\sqrt[4]{x} .\end{array}