this post was submitted on 11 Oct 2023
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Simpler: x^1 = x, x^-1 = 1/x
x^1 * x^-1 = x^0 = x/x = 1.
Of course, your explanation is the "correct" one - why it's possible that x^0=1. Mine is the simple version that shows how logic checks out using algebraic rules.
Of course you both assume x =/= 0 though.