Answer
$13s^2t^{5}\sqrt{s}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt{169s^5t^{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 results to
\begin{array}{l}\require{cancel}
\sqrt{169s^4t^{10}\cdot s}
\\\\=
\sqrt{(13s^2t^{5})^2\cdot s}
\\\\=
13s^2t^{5}\sqrt{s}
.\end{array}