# Simple question on exponentiation

I know this one is trivial, but I was wondering: if I have something like $$a^{b^c}$$ then i know that it should be read as $$a^{\left(b^c\right)}$$ if no other parenthesis is present.

Question: if $a=k^2$ for some $k\in\mathbb{N}$, $b=h^2$ for some $h\in\mathbb{N}$, and $c=j^2$ for some $j\in\mathbb{N}$, does the following relation stand true? $$a^{b^c}=k^{k^{h^{h^{j^j}}}}=k^{k\cdot h\cdot h\cdot j\cdot j}$$

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No, if $a = c = 4 = 2^2$ and $b = 1 = 1^2$, then the left hand side is $4^{1^4} = 4^1 = 4$, and the right hand side is $2^{8} \not= 4$.
Take $b = 4$ as well then. Then the right hand side is 4294967296 while the left hand side is 13407807929942597099574024998205846127479365820592393377723561443721764030073546‌​976801874298166903427690031858186486050853753882811946569946433649006084096. –  fuglede Apr 16 at 12:12
$$a^{b^{c}}=\left(k^{2}\right)^{\left(h^{2}\right)^{(j^{2})}}=\left(k^{2}\right)^{h^{2j^{2}}}=k^{2h^{2j^{2}}}$$ Based on: $$\left(r^{s}\right)^{t}=r^{st}$$