problem: When $(x\sqrt{x^3})^4$ is simplified, what is the exponent of $x$?
solution: 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 $\boxed{10}$.