Answer
$\dfrac{x^2y\sqrt{xy}}{z}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt{\dfrac{x^5y^3}{z^2}}
,$ find a factor of the radicand that is a perfect power of the index. Then, extract the root of that factor.
$\bf{\text{Solution Details:}}$
Factoring the expression that is a perfect power of the index and then extracting the root result to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{x^4y^2}{z^2}\cdot xy}
\\\\=
\sqrt{\left( \dfrac{x^2y}{z} \right)^2\cdot xy}
\\\\=
\left|\dfrac{x^2y}{z}\right| \sqrt{xy}
.\end{array}
Since all variables are assumed to be positive, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{x^2y}{z}\sqrt{xy}
\\\\=
\dfrac{x^2y\sqrt{xy}}{z}
.\end{array}
