algebra precalculus - Simplify this expression fully

How would i simplify fully the following expression?

$\dfrac{{\sqrt 2}({x^3})}{\sqrt{\frac {32}{x^2}}}$

So far i have got this

$\dfrac{{\sqrt 2}{x^3}}{{\frac{\sqrt 32}{\sqrt x^2}}}$ = $\dfrac{{\sqrt 2}{x^3}}{{\frac{4\sqrt 2}{x}}}$

Am not quite sure if this is correct however, could someone help explain how i would simplify this expression?

Answer

There is a mistake in the OP. Recall that $\sqrt{x^2}=|x|\ne x$ when $x<0$. To simplify, we can write

$$\frac{\sqrt 2 x^3}{\sqrt{\frac{32}x}}=\frac{\sqrt 2 x^3}{\frac{4\sqrt 2}{|x|}}=\frac{x^3|x|}{4}$$