Answer
$\dfrac{4\sqrt{x}}{x^4}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{4}{\sqrt{x^7}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4}{\sqrt{x^7}}\cdot\dfrac{\sqrt{x}}{\sqrt{x}}
\\\\=
\dfrac{4\sqrt{x}}{\sqrt{x^8}}
\\\\=
\dfrac{4\sqrt{x}}{\sqrt{(x^4)^2}}
\\\\=
\dfrac{4\sqrt{x}}{x^4}
.\end{array}
Note that all variables are assumed to represent positive real numbers.