# Simplyfing a quotient of polynomials [closed]

I am trying to simplify some quotient of polynomials. In this case, they are really easy but I will have to deal with way harder expression and I wanna know how to do it in full generality. An example is

This is just

$$\begin{equation} (z_1-z_2)^{-h-2}\left(\frac{(z_1-z_2)(z_3-z_4)}{(z_1-z_3)(z_2-z_4)}\right)^{2+h}\left(\frac{z_1-z_4}{z_1-z_3}\right)^{2-h}\left(\frac{z_2-z_4}{z_1-z_4}\right)^{2-h}(z_3-z_4)^{-2-h} \end{equation}$$

Simplify[(z1 - z2)^(-2-h) ( (((z1 - z2) (z3 - z4))/((z1 - z3) (z2 - z4)))^(2
+ h)) ((z1 - z4)/(z1 - z3))^(2 - h) ((z2 - z4)/(z1 - z4))^(2 - h) (z3 - z4)^(-2 - h)]


This should just simplify to $$\frac{1}{(z_2-z_4)^{2h}}\frac{1}{(z_1-z_3)^{4}}$$. I understand that Mathematica is afraid and don't want to simplify everything, even if given the fact that h is an integer. Is there someone that know what to do to get the final simplification ?

• Use PowerExpand[]. Oct 3 '18 at 13:21
• @ J.M. is somewhat okay, Thank you very much Oct 3 '18 at 14:08