Radical Mad

$x^{\sqrt x}=729=9^3=9^{\sqrt 9}\color{#3D99F6}{\implies x=9}$

$y^{\sqrt y}=65536=16^4=16^{\sqrt{16}}\color{#3D99F6}{\implies y=16}$

$z^{\sqrt z}=16=4^2=4^{\sqrt 4}\color{#3D99F6}{\implies z=4}$

Therefore equations are:

$\begin{cases}\sqrt{a+b}=3~(**)\implies a+b=9\\\sqrt{a-b}=1\implies a-b=1\end{cases}$

Adding and subtracting we get $\color{#3D99F6}{a=5\color{#333333}{,}b=4}$ .

$\therefore x+y+z+a+b-2=36$

and we are required to find:

$\large 36^{\frac{\sqrt{36}}3}=36^2=\boxed{\color{#69047E}{1296}}$

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$(**)$ Having found $\sqrt{a+b}=3$ , squaring we get $\color{#D61F06}{a+b=9}$ . Hence $x+y+z+\color{#D61F06}{a+b}-2=9+16+4+\color{#D61F06}{9}-2=36$ . And then we have to find $36^{\sqrt{36}/3}=1296$

Hence we do not require equation $x+y+z+\sqrt{a-b}=30$