TITLE: When (and why) did the convention that exponents are evaluated from right to left arise?
QUESTION [5 upvotes]: Earlier, I saw this question on Quora: X^Y^Z Which one do I do first? and the current most-upvoted answer is this:

The ^ operator is not associative, so that:
(X^Y)^Z is not the same value as X^(Y^Z)
For some reason, the convention for exponents is to apply from the top down (or right to left), so that
X^Y^Z = X^(Y^Z)
I am not sure why this is the case.  It's just a convention.

That is, $3^{3^3}=3^{27}=7625597484987$, not $27^3=19683$. So, why is it convention to evaluate a power tower from right to left and when did it arise?

REPLY [4 votes]: $(a^b){}^{{}^c}$ is the same as $(a^b)^c=a^{bc}$. If it was evaluated left-to-right, we'd have $a^{b^c}=a^{bc}$, so power towers would do nothing.
The way it's usually done, from right to left, has $a^{b^c}\ne a^{bc}$. Ultimately, that's what it comes down to.

EDIT: As mentioned elsewhere, right-to-left is the only way for something like $e^{x^2+1}$ to make sense. That hadn't occurred to me. (EDIT: This stops being a relevant point if we write exponentiation as $a\text^b$ instead of $a^b$, as you've done in part of the question — you'd write it as $e\text^(x\text^2+1)$, and the parentheses tell you how to evaluate it.)