Answer
$\dfrac{1}{x^{2}}$
Work Step by Step
Using laws of exponents, then,
\begin{array}{l}
\dfrac{(x^3)^{1/2}}{x^{7/2}}
\\\\=
\dfrac{x^{3\cdot\frac{1}{2}}}{x^{\frac{7}{2}}}
\\\\=
\dfrac{x^{\frac{3}{2}}}{x^{\frac{7}{2}}}
\\\\=
x^{\frac{3}{2}-\frac{7}{2}}
\\\\=
x^{-\frac{4}{2}}
\\\\=
x^{-2}
\\\\=
\dfrac{1}{x^{2}}
.\end{array}
