Answer
$x^3y^4\sqrt[]{13x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[]{13x^7y^8}
,$ 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[]{x^6y^8\cdot13x}
\\\\=
\sqrt[]{(x^3y^4)^2\cdot13x}
\\\\=
x^3y^4\sqrt[]{13x}
.\end{array}