## Intermediate Algebra (12th Edition)

$2q^2\sqrt[3]{5q}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $6q^2\sqrt[3]{5q}-2q\sqrt[3]{40q^4} ,$ 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} 6q^2\sqrt[3]{5q}-2q\sqrt[3]{8q^3\cdot5q} \\\\= 6q^2\sqrt[3]{5q}-2q\sqrt[3]{(2q)^3\cdot5q} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 6q^2\sqrt[3]{5q}-2q(2q)\sqrt[3]{5q} \\\\= 6q^2\sqrt[3]{5q}-4q^2\sqrt[3]{5q} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (6q^2-4q^2)\sqrt[3]{5q} \\\\= 2q^2\sqrt[3]{5q} .\end{array}