Proof That x^-n is equal to 1/(xⁿ)

Before showing the proof, there are two things you must know:

Lets call these two our first and second axioms. What we are trying to prove is this:

We can write this as:

Using the first axiom, we can do this:

If we simplify this, we get:

And this matches with our second axoims, proving that [x^-n is equal to 1/(xⁿ)].