Most of us know that multiplication is repeated addition and that exponentiation is repeated multiplication.
You will notice if you begin solving certain problems that addition and multiplication are commutative, but suddenly exponentiation is not commutative. For example:
$2^3 = 8$
$3^2 = 9$
$8$ is not equal to $9$
My question is, are there operations beyond exponentiation that are commutative (I know tetration is the next operation after exponentiation, but I'm pretty sure it's not commutative)? If there are, what are they? If not, do we know why there aren't any?