exponentiation - Why does any nonzero number to the zeroth power = 1?

I can't properly wrap my head around this odd concept, though I feel I'm almost there.

A non-zero base raised to the power of 0 always results in 1.
After some thinking, I figured this is the proof:
$\frac{{x}^{2}}{{x}^{2}}= x^{2-2}=x^{0}=1$

Assuming that's true, would it be correct to assume that anything raised to 0 is a "whole" (1)? Because if $\frac{{x}^{2}}{{x}^{2}}=1$, then no matter what x is, it will always result in 1.

I would like to understand this concept intuitively and deeply, rather than just memorizing that $x^{0}=1$

EDIT: Thank you all for the answers. Each and everyone of them have been insightful and I've now gained a deeper understanding. This is a new account, so it seems I can't upvote, but if I could I would upvote each and everyone of you. Thanks :)

Answer

Here's a good heuristic that helped me feel better about it back in the day:

Consider any number $x$ to any power. We will choose, say, $5^3$.

$5^3 = 125$. Divide both sides by $5$. You get $5^2=25$, which we know. Again. Then you get $5^1=5$. We usually leave exponents of $1$ off but we'll keep it here. Do you see what happens? The power goes down by $1$ each time. We can do it again. Then following our pattern, $5^0=1$. But $5$ wasn't special!

You can do this with any real number. Of course, for irrationals it can get a little fuzzy.

By the way, we can keep going. Divide by $5$ again. You get $5^{-1}=\frac{1}{5}$. I hope this helps!