Answer
$12m\sqrt[3]{m}+15m\sqrt[4]{m}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
