#### Answer

$\frac{\sqrt[3] 3}{4}$

#### 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, $\sqrt[3] (\frac{3}{64})=\frac{\sqrt[3] 3}{\sqrt[3] 64}=\frac{\sqrt[3] 3}{4}$
We know that $\sqrt[3] 64=4$, because $4^{3}=64$.