How can I find the density function of Z?

Question

I am trying to find the density function for Z, this is what I am doing but I am not getting an appropiate function, I don´t know if there is something wrong with limits of the intregral. Or if this is not the correct approach. I have that $f(x)=ax^{a-1}$ for $0<x<1$ and $a>0$ and X and Y are iid, so I say that $f(y)=ay^{a-1}$ and $f(x,y)=a^2x^{a-1}y^{a-1}$

Answer 1

The limits of the inner integral should be between 0 and $\min(Z/Y,1)$.