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a^(2^n)

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a^(2^n) 2010-10-22
From Tim:
I am trying to understand a^(2^n). The hint they give is a^(2^(n+1)) = (a^(2^n))^2 I am writing a program that will solve a^(2^n) recursively but need to understand the power before I begin. I am currently pursuing writing (a) x (a^(2^(n-1))) where the (a^(2^(n-1))) would be the recursive function call a n approaches 0. Once n is 0, the result would be multiplied by a two more times. Anyway, explaining these powers would be appreciated. I will most likely complete the program before the answer but I want to understand the logic of these powers. Thank you, Tim
Answered by Stephen La Rocque.
 
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