How many ordered triples of positive integers (x,y,z) satisfy (x^y)^z=64

Please answer and explain asap! Thanks!

64 = (64^1)^1 = (8^2)^1 = (4^3)^1 = (2^6)^1
By symmetry, there are 9 ordered triples: (64, 1, 1), (8, 2, 1), (8, 1, 2), (4, 3, 1), (4, 1, 3), (2, 6, 1), (2, 1, 6), (2, 2, 3), (2, 3, 2).