Answer
$\dfrac{3\sqrt{x}}{x^2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{\dfrac{9}{x^3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{9}{x^2}\cdot\dfrac{1}{x}}
\\\\=
\sqrt{\left(\dfrac{3}{x}\right)^2\cdot\dfrac{1}{x}}
\\\\=
\dfrac{3}{x}\sqrt{\dfrac{1}{x}}
\\\\=
\dfrac{3}{x}\sqrt{\dfrac{1}{x}\cdot\dfrac{x}{x}}
\\\\=
\dfrac{3}{x}\sqrt{\dfrac{x}{x^2}}
\\\\=
\dfrac{3}{x}\cdot\dfrac{\sqrt{x}}{\sqrt{x^2}}
\\\\=
\dfrac{3}{x}\cdot\dfrac{\sqrt{x}}{x}
\\\\=
\dfrac{3\sqrt{x}}{x^2}
.\end{array}
Note that all variables are assumed to represent positive real numbers.
