aLgEbrA

Let $P = 4^{1/4} \cdot 16^{1/16} \cdot 64^{1/64} \cdot 256^{1/256} \dotsm$
Then $P$ can be expressed in the form $\sqrt[a]{b}$ where $a$ and $b$ are positive integers. Find the smallest possible value of $a+b$