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

Think of it as 0 = n – n

So x to the power of 0 is x to the power of (n -n)

So

X^0 = x^(n-n)

Which is x^n ÷ x^n

Thus by definition it is 1 unless x is 0.