ELI5, how does 2^0 power equal 1?

Question

I’m doing my GED and passed that math part but this never came up. I saw it on a meme and am lost.
Help!!??

In: 9770

Answer 1

Anything to the power of 0 is 1 by definition. We decided to do that because it makes it consistent with all the properties of exponentiation.
For example,
x^(a-b) = x^a / x^b, so if a=b, then x^(a-a) = x^a / x^a, so x^0 = 1

We took it further, and also defined the operation for negative numbers, so x^(-n) = 1/x^n, because x^(-n) * x^n should equal x^(-n+n) = x^0 = 1.

We have similar definitions for rational numbers, etc. So even though the basic definition is multiply a number n times, we can generalize it in ways that make sense.