Prove that $ x^xy^y=z^z $ has infinite integral solutions

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Show that there exist an infinite number of solutions for $$ x^xy^y=z^z $$ where $x,y,z \gt 1$ & $x,y,z\in \mathbb Z$

I don't know how to even start,infact I am not able to find a particular solution of this problem let alone infinite.How to approach?