Answer
$\dfrac{5\sqrt{y}}{7y}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{5\sqrt{x}}{7\sqrt{xy}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5}{7}\sqrt{\dfrac{x}{xy}}
\\\\=
\dfrac{5}{7}\sqrt{\dfrac{\cancel{x}}{\cancel{x}y}}
\\\\=
\dfrac{5}{7}\sqrt{\dfrac{1}{y}}
\\\\=
\dfrac{5}{7}\sqrt{\dfrac{1}{y}\cdot\dfrac{y}{y}}
\\\\=
\dfrac{5}{7}\sqrt{\dfrac{y}{y^2}}
\\\\=
\dfrac{5}{7}\cdot\dfrac{\sqrt{y}}{\sqrt{y^2}}
\\\\=
\dfrac{5}{7}\cdot\dfrac{\sqrt{y}}{y}
\\\\=
\dfrac{5\sqrt{y}}{7y}
.\end{array}
Note that all variables are assumed to represent positive real numbers.