Why Is Exponentiation Associative?

Exponentiation to the power of any positive integer can be defined consistently whenever multiplication is power-associative. ... Exponentiation to the power of zero can also be defined if the operation has an identity element, so the existence of identity elements is useful in power-associative contexts.

Why is exponentiation right associative?

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 x^yz should be read as x^(yz), not (x^y)^z.

Is exponentiation associative or commutative?

So exponentiation is not commutative because its "successor" is not 1. This also explains why exponentiation is commutative for e.g. 22, since 2−1=1, and so we have a unit successor.