Answer
$-3r^{3}s^{2}\sqrt[4]{2r^3s^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
-\sqrt[4]{162r^{15}s^{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[4]{81r^{12}s^{8}\cdot2r^3s^2}
\\\\=
-\sqrt[4]{(3r^{3}s^{2})^4\cdot2r^3s^2}
\\\\=
-3r^{3}s^{2}\sqrt[4]{2r^3s^2}
.\end{array}