If an expression was (x * y)^n , so (x times y) to the power of n, would you multiply x and y first or distribute the exponent, making (x^n * y^n)?

Either order is correct.

Small example: let's take . Then



By the commutative property, we can write



By the associative property, we can regroup consecutive terms.




By the associative property again, we can regroup terms and write



Commutativity:



Associativity:




You can show by induction that this holds in general for so that .