Answer
$2x\sqrt[4]{3x}$.
Work Step by Step
Factor the radicand so that some factors are fourth powers.
$=\sqrt[4]{16x^4\cdot 3x}$
Use $16=2^4$.
$=\sqrt[4]{2^4x^4\cdot 3x}$
Use $2^4x^4=(2x)^4$.
$=\sqrt[4]{(2x)^4\cdot 3x}$
Separate using the rule $\sqrt[n]{a\cdot b}=\sqrt[n]{a} \cdot \sqrt[n]{b}, a>,b>0:$
$=\sqrt[4]{(2x)^4}\cdot \sqrt[4]{3x}$
Simplify.
$=|2x| \sqrt[4]{3x}$
$=2x\sqrt[4]{3x}$
Hence, the correct answer is $2x\sqrt[4]{3x}$.
