Answer
$-3mn^{3}\sqrt[3]{3mn}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[3]{-81m^4n^{10}}
,$ 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]{-27m^3n^{9}\cdot3mn}
\\\\=
\sqrt[3]{(-3mn^{3})^3\cdot3mn}
\\\\=
-3mn^{3}\sqrt[3]{3mn}
.\end{array}