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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 ?

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closed as off-topic by mikado, Bob Hanlon, m_goldberg, rhermans, José Antonio Díaz Navas Oct 15 '18 at 10:04

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    $\begingroup$ Use PowerExpand[]. $\endgroup$ – J. M. is away Oct 3 '18 at 13:21
  • $\begingroup$ @ J.M. is somewhat okay, Thank you very much $\endgroup$ – Ezareth Oct 3 '18 at 14:08