Why is exponentiation applied right to left?

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The ** operator follows normal mathematical conventions; it is right-associative:

In the usual computer science jargon, exponentiation in mathematics is right-associative, which means that xyz should be read as x(yz), not (xy)z. In expositions of the BODMAS rules that are careful enough to address this question, the rule is to evaluate the top exponent first.

and from Wikipedia on the Order of Operations:

If exponentiation is indicated by stacked symbols, the usual rule is to work from the top down, because exponention is right-associative in mathematics.

So 2 ** 3 ** 4 is calculated as 2 ** (3 ** 4) (== 2417851639229258349412352) not (2 ** 3) ** 4 (== 4096).

This is pretty universal across programming languages; it is called right-associativity, although there are exceptions, with Excel and MATLAB being the most notable.

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