Erdős problem 674

Are there any integer solutions to $x^xy^y=z^z$ with $x,y,z>1$?

Ko [Ko40] proved there are none if $(x,y)=1$, but there are in fact infinitely many solutions in general - for example, $x=2^{12}3^6$, $y = 2^83^8$, and $z = 2^{11}3^7$.