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

Revise the law of indices which states,

x^n / x^m = x^(n – m)

So,
x^0 = x^(1 – 1) = x^1 / x^1 which cancels to 1.

Hence proved