I'm no authority on exponential subject matter, but I've been told numerous times that any integer to the 0 power equals one.

My reasoning for this is that the identity property states that a variable * 1 equals 1. With the 0 power the integer is not being multiplied at all, multiple times or otherwise, but 1 can be implied by the identity property.

Once again, I'm not an authority but this is just my input. I can be wrong by any means.

I am reasonably familiar with calc, though by no means great at it - no need to apologize anyway (I'll admit that I haven't come across the seven undefined operations at all yet). This is genuinely something that confuses me though, I actually want to know why this operation throws out different answers under different situations and what those situations are. Plus some people here are pretty smart

I believe I've just confused myself so let me provide some visuals.

Let's take 3^2.  This notation can be interpreted as 3 * 3.  By the identity property, it can noted as 1 * 3 * 3 without changing the meaning.  Now when you have something like 3^0, 3 does not appear in the interpretation so by the identity it's basically saying 1 *.  I believe the same would be true with 0^0.

Yet again, I'm not an authority.

1

Hi, I'm a math minor and the wife has a BA in Math.  What crazy classes did you take that made you do papers on math?

For all intents and purposes, go with 0^0=1.

Something similar:

0! = 1

Whoops, also forgot to mention I had never actually heard this problem and just assumed it would be 1 but the wiki has a pretty explanation on why it would be undefined.

0^x is 0 for a x > 0

x⁰ is 1 for all x > 0

0⁰ isn't defined for both of those cases together therefore it's undefined.  Of course I'm also fine with just calling it 1.