Radical Mad

Algebra Level 3

If \(x^\sqrt{x}=729\), \(y^\sqrt{y}=65536\), \(z^\sqrt{z}=16\), \(x+y+z+\sqrt{a+b}=32\) and \(x+y+z+\sqrt{a-b}=30\), then find

\[\large (x+y+z+a+b-2)^{\frac {\sqrt{x+y+z+a+b-2}} 3}\]