When $(x\sqrt{x^3})^4$ is simplified, what is the exponent of $x$?
We have  \begin{align*}
(x\sqrt{x^3})^4 &=(x\cdot x^{\frac{3}{2}})^4\\
&=(x^{1+\frac{3}{2}})^4\\
&= (x^{\frac{5}{2}})^4\\
&= x^{\frac{5}{2}\cdot4}\\
&= x^{10}
\end{align*} So, the exponent of $x$ is $\boxed{10}$.