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This question had me initially when I tried to do it in hurry, but I think I figured it out, another one of those where you have to consider lot of cases

Ok case 1 is easy: say x =9, y = 2, z = 1 then x > y^2 > z^4

Suppose X = 9, Z = 1/2, y = -1 or x >z >y, case 3
Then x > y^2 > z^4

Suppose z = 0.6, then Z^4 = 0.1296, y = 0.5, then y = 0.25, x = 0.4