Answer
$-10r^{5}\sqrt[]{5r}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
-\sqrt[]{500r^{11}}
,$ 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[]{100r^{10}\cdot5r}
\\\\=
-\sqrt[]{(10r^{5})^2\cdot5r}
\\\\=
-10r^{5}\sqrt[]{5r}
.\end{array}