eli5: why is x⁰ = 1 instead of non-existent?

Question

It kinda doesn’t make sense.
x¹= x

x² = x*x

x³= x*x*x

etc…

and even with negative numbers you’re still multiplying the number by itself

like (x)-² = 1/x² = 1/(x*x)

In: 1797

Answer 1

In addition to other comments, I’d like to add that powers of 10 are helpful for remembering this for me — since the rule is, for powers of 10, the exponent tells you how many 0’s are in the number. Positive exponents, the 0’s come after the 1; negative, they come before. But if the exponent itself is 0, well, there are no 0’s, before or after the 1. It’s just a 1 🙂