jmc

We can first rewrite the term under the fifth root: $x\sqrt{x^3}=x\cdot x^{3/2}=x^{5/2}$. Then we simplify the entire expression on the left side of the equation, which gives $\sqrt[5]{x^{5/2}}=(x^{5/2}{)}^{1/5}=x^{(5/2)\cdot (1/5)}=x^{1/2}$. We now have $\sqrt{x}=3$ and we can square each side to find $x=\boxed{9}$.