Answer
$x+x^2$
Work Step by Step
Using the Distributive Property and the laws of exponents, then,
\begin{array}{l}
x^{1/2}(x^{1/2}+x^{3/2})
\\\\=
x^{\frac{1}{2}+\frac{1}{2}}+x^{\frac{1}{2}+\frac{3}{2}}
\\\\=
x^{\frac{2}{2}}+x^{\frac{4}{2}}
\\\\=
x+x^2
.\end{array}