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

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

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A)

64 = 2^6 = 4^3 = 8^2 = 64^1. 

2 = 2^1; 
4 = 2^2 = 4^1; 
8 = 2^3 = 8^1; 

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).

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