For subtraction I can understand why $2-3 = 2+(-3)$ since we read from left to right, but I don't see why this need apply to exponentiation. What benefit is there to writing the base before the exponent? With addition and multiplication order doesn't matter since $a+b=b+a$, so why was $a^n$ chosen, and who popularised this notation?
A similar question, with the focus on the historical reasons, has also been asked on History of Science and Math.
On
I'm going to say that it's also because of the way we read.
$2^3$ is "two to the cube" or "two to the third" whereas $^23$ would be "to two, the three?".
Of course, this could be very bad reason since you can argue that the operation $3^2$ existed before we decided to read it...
(I wanted to write this as a comment better than a proper answer, but I can't write comments yet I'm afraid)
Wikipedia says "The modern notation for exponentiation was introduced by René Descartes in his Géométrie of 1637", and has a link to a page from Descartes.