Why does x^0 = 1 and x^(-n) = 1/x^n? (Index)

I’m using the Twelve Days of Christmas (and perhaps a few extra days besides) to do something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series why the rules for x^0 and x^{-n} work the way they do.

Part 1: Multiplication and division.

Part 2: The Laws of Exponents.

 

 

 

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