Powers in ASCII text

Question

I have a problem reading a discussion forum post. Namely, in the ASCII text, is 2^3^4 the same as $(2^3)^4$ or $2^{3^4}$?

Answer 1

I believe that usually the intended meaning of a^b^c or $a^{b^c}$ is $a^{(b^c)}$.

The reason is that if someone wants to write $(a^b)^c$, he can use the equivalent expression $a^{bc}$ instead.

In particular, this seems to be quite common in cardinal arithmetic - I think no one will doubt what is meant when someone writes $2^{2^{\aleph_0}}$ even when it's not indicated by brackets: $2^{(2^{\aleph_0})}$.

Answer 2

The reason you have a problem is that the notation is ambiguous. A careful writer will write 2^(3^4) or (2^3)^4, depending on what she means. There is no way of telling what 2^3^4 means, except possibly from context.