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

since the other explanations perhaps didn’t take / didn’t address the fundamental concept/feeling/intuition:

consider the power operator to do the following:

2^3 = 1*2*2*2

as in 1 * (multiply 2 by itself 3 times)

2^0 = 1 (followed by no multiplications of 2)

1* (multiply 2 by itself 0 times) = 1.