Answer
$ x\sqrt[4]{2}$
Work Step by Step
Apply $ \displaystyle \qquad \frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$
$\displaystyle \frac{\sqrt[4]{32x^{5}}}{\sqrt[4]{16x}}=\sqrt[4]{\frac{32x^{5}}{16x}} $
$=\sqrt[4]{\frac{32}{16}\cdot x^{5-1}} $
$=\sqrt[4]{2\cdot x^{4}}$
$=\sqrt[4]{2}\cdot\sqrt[4]{x^{4}}$
Apply $ \sqrt[n]{x^{n}}=|x^{n}|,$ when n is even.
Since we assume x is positive:
= $\sqrt[4]{2}\cdot x $
