Answer
$4$
Work Step by Step
RECALL:
(1) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
(2) If $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers, then $\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{ab}$.
Use the rules above to obtain:
\begin{align*}
16^{\frac{1}{3}} \cdot 4^{\frac{1}{3}}&=\sqrt[3]{16} \cdot \sqrt[3]{4}\\
&=\sqrt[3]{16(4)}\\
&=\sqrt[3]{64}\\
&=\sqrt[3]{4(4)(4)}\\
&=\sqrt[3]{4^3}\\
&=4
\end{align*}
