## Intermediate Algebra (12th Edition)

$18\sqrt[3]{2m}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $6\sqrt[3]{128m}-3\sqrt[3]{16m} ,$ 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} 6\sqrt[3]{64\cdot2m}-3\sqrt[3]{8\cdot2m} \\\\= 6\sqrt[3]{(4)^3\cdot2m}-3\sqrt[3]{(2)^3\cdot2m} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 6(4)\sqrt[3]{2m}-3(2)\sqrt[3]{2m} \\\\= 24\sqrt[3]{2m}-6\sqrt[3]{2m} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (24-6)\sqrt[3]{2m} \\\\= 18\sqrt[3]{2m} .\end{array}