13. How many ordered triples of positive integers $(x, y, z)$ satisfy $\left(x^{y}\right)^{z}=1024$ ?
SolUtion
009

Note that $1024=2^{10}$, so we require $y z$ to be a factor of 10 . Hence the solutions are $(1024,1,1),(32,2,1),(32,1,2),(4,5,1),(4,1,5),(2,10,1),(2,1,10)$, $(2,5,2),(2,2,5)$