Is this identity true: $2^{2^n}= 4^n$? I believe this is true as far as I know. Sorry this is the only place to ask.
Is there another identity for $2^{2^n}$ which I can simplify to?
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3The ordinary meaning of $2^{2^n}$ is $2^{(2^n)}$, in which case the equality fails. – André Nicolas Oct 12 '15 at 04:02
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But isn't 2^(2^n) = (2^2)^n? Is there another identity for $2^{2^n}$? – Ka Wa Yip Oct 12 '15 at 04:04
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1$2^{2^n}=2^{(2^n)}=4^{(2^{n-1})}=4^{2^{n-1}}$. – Ramiro Oct 12 '15 at 04:07
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No. In standard usage, $2^{2^n}$ means $2^{(2^n)}$, not $(2^2)^n$.
Notice that $(a^b)^c$ is equal to $a^{bc}$, whereas $a^{(b^c)}$ cannot be similarly simplified.
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Hint: What happens when $n = 0$?
Advice:
Also, before asking simple questions like these, it is a good idea to try out a few values.
balddraz
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A compiler — i.e., a computer program that translates a program written in a high-level language into a machine-level language — treats a^b^c as a^(b^c) rather than as (a^b)^c, (as the OP speculated).
Senex Ægypti Parvi
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