Joint distribution of ratio of uniform distribution

Question

If $X \sim \mathrm{Uniform}[X_{\min}, X_{\max}]$ and $Y \sim \mathrm{Uniform}[Y_{\min}, Y_{\max}]$, then what does the p.d.f of $Z = X^a/Y$ look like? I think it is a function that is segmented.

Thanks a lot!