Can somebody explain the rules of algebra so that the following expression makes sense:

$\displaystyle 2^{2 \cdot 2^m}+1$ $\displaystyle =\left(2^{2^m}\right)^2+1$

I thought that $\displaystyle \left(2^{2^m}\right)^2+1$ $\displaystyle =4^{ \cdot 4^(m^2)}+1$ but apparently thats wrong.