I'm trying to verify my solution to this problem:

Suppose $\displaystyle a$ and $\displaystyle x$ are both elements in group $\displaystyle G$. Solve the following equations simultaneously for $\displaystyle x$:

$\displaystyle x^2=a^2$ and $\displaystyle x^5=e$ where $\displaystyle e$ is the identity element of $\displaystyle G$

OK. I find that $\displaystyle x=(a^4)^{-1}$.

I'm having trouble verifying this result. CAN I verify?

*note: $\displaystyle x*x=x^2$ is an example of the notation employed here.