Answer
$\color{blue}{32\sqrt[3]{2}}$
Work Step by Step
Note that $(-2)^4=16$ and $16=2^4$.
Thus, the given expression is equivalent to:
$=\sqrt[3]{2^4(16)(2^8)}
\\=\sqrt[3]{2^4\cdot2^4\cdot2^8}$
Use the rule $a^m\cdot a^n = a^{m+n}$ to obtain:
$=\sqrt[3]{2^{4+4+8}}
\\=\sqrt[3]{2^{16}}$
Factor the radicand so that one factor is a perfect cube to obtain:
$=\sqrt[3]{(2^{15})(2)}
\\=\sqrt[3]{(2^5)^3(2)}$
Bring out the cube root of the perfect cube factor to obtain:
$=2^5\sqrt[3]{2}
\\=\color{blue}{32\sqrt[3]{2}}$
