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

You get square of x by multiplying x by x. The cube of x by multiplying the square by x and so in. So what would you need to multiply x with, to get x

Think of it as

x^n =x^(n-1) *x

So

x^(n-1)=(x^n) /x

Now replace n by 1.