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 \(a+b\)
By telescoping product, $P = 2^{5/3} = \sqrt[3]{32}$, so $a + b = 32 + 3 = \boxed{35}$.
