We find that $f(1) = 2^1 = 2.$ Then, $f(f(1)) = f(2) = 2^2 = 4$ and $f(f(f(1))) = f(4) = 2^4 = 16.$ Therefore, $f(f(f(f(1)))) = f(16) = 2^{16}$ and so $\sqrt{f(f(f(f(1))))} = \sqrt{2^{16}} = 2^8 = \boxed{256}.$
Question:
Let $f(x) = 2^x.$ Find $\sqrt{f(f(f(f(1))))}.$
Answer:
Let's think step by step.

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256
Let $f(x) = 2^x.$ Find $\sqrt{f(f(f(f(1))))}.$
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