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

 
 Sep 11, 2021

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