<s>[INST] 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?
 [/INST] $\frac{\sqrt{2}x^3}{\sqrt{\frac{32}{x^2}}} = \frac{\sqrt{2}x^3}{\frac{\sqrt{32}}{\sqrt{x^2}}} = \frac{\sqrt{2}x^3}{\frac{4\sqrt{2}}{x}} = \frac{x^3}{\frac{4}{x}} = \frac{x^4}{4}$
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