Answer
$\dfrac{\sqrt{7}}{x}$
Work Step by Step
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $
\sqrt{\dfrac{7}{x^4}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{7}}{\sqrt{x^4}}
\\\\=
\dfrac{\sqrt{7}}{\sqrt{(x^2)^2}}
\\\\=
\dfrac{\sqrt{7}}{x}
.\end{array}
Note that variables are assumed to have positive real numbers.
