#### Answer

$-5t^3s^{10}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
-\sqrt[]{25t^6s^{20}}
,$ 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 results to
\begin{array}{l}\require{cancel}
-\sqrt[]{(5t^3s^{10})^2}
\\\\=
-5t^3s^{10}
.\end{array}