Answer
$\frac{\sqrt[3] 3}{2x^{2}}$
Work Step by Step
The quotient rule holds that $\sqrt[n] (\frac{a}{b})=\frac{\sqrt[n] a}{\sqrt[n] b}$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero).
Therefore, $\sqrt[3] (\frac{3}{8x^{6}})=\frac{\sqrt[3] 3}{\sqrt[3] (8x^{6})}=\frac{\sqrt[3] 3}{2x^{2}}$
We know that $\sqrt[3] (8x^{6})=2x^{2}$, because $(2x^{2})^{3}=(2\times2\times2)\times x^{2+2+2}=8x^{6}$.
