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

Simplest answer.

Any number x can be rewritten as x*1.

So x^n = x * x *…x*1

Whether the number of x is equal to n. So write out x^0 in the same way.

x^0 = 1