Answer
$4x\sqrt[3]{x}+6x\sqrt[4]{x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
