An interesting equation

The same question has been posted by Mr. Calvin Lin. Nevertheless the solutions are

$\large 4^{2}=2^{4}$

$\large 2^{4}=4^{2}$

$\large -2^{-4}=-4^{2}$

$\large -4^{-2}=-2^{-4}$

The only four solutions I could find are $(1,-1),(-1,1),(2,4)$ and $(4,2)$ .