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# aLgEbrA

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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 $$a+b$$

Sep 11, 2021

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