#### Answer

$-2zt^2\sqrt[3]{2z^2t}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[3]{-16z^5t^7}
,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers.
$\bf{\text{Solution Details:}}$
Expressing the radicand of the expression above with a factor that is a perfect power of the index and then extracting the root of that factor results to
\begin{array}{l}\require{cancel}
\sqrt[3]{-8z^3t^6\cdot 2z^2t}
\\\\=
\sqrt[3]{(-2zt^2)^3\cdot 2z^2t}
\\\\=
-2zt^2\sqrt[3]{2z^2t}
.\end{array}