Answer
$\dfrac{5\sqrt{14x}}{21x}$
Work Step by Step
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index, the given expression is equivalent to
\begin{align*}\require{cancel}
&
=\dfrac{5\sqrt{2}}{3\sqrt{7x}}\cdot\dfrac{\sqrt{7x}}{\sqrt{7x}}
\\\\&=
\dfrac{5\sqrt{14x}}{3\sqrt{7^2x^2}}
\\\\&=
\dfrac{5\sqrt{14x}}{3\sqrt{(7x)^2}}
\\\\&=
\dfrac{5\sqrt{14x}}{3(7x)}
\\\\&=
\dfrac{5\sqrt{14x}}{21x}
.\end{align*}
Hence, the simplified form of the given expression is $
\dfrac{5\sqrt{14x}}{21x}
$.
