For zero to the zeroth being zero and zero to the zeroth power being one.

What happens at zero to the zeroth power?

We look in the zeroth component for the type.

And for Galois this was like the zeroth symmetry.

Let's think about what zero to the zeroth power is,

And so you might say, anything to the zeroth power is one, so i to the zeroth power is one, and that is true.

So with that said, 1 to the zeroth power is just going to be 1. Anything other than zero to the zeroth power is 1.

Maybe you should say zero to the zeroth power is zero.

The zeroth part was identifier , so the oneth part is x .

Maybe zero to the zeroth power is going to be equal to one.

Zero to the zeroth is not defined by, at least, more conventional mathematics.

So I could start with, lets start with i to the zeroth power.

We're going to extract it, by getting the zeroth element of the (tree).

Now, there is one rule before the first rule, that's the zeroth rule.

Any non zero number to the zeroth power you are going to get one.

So we'll go to the zeroth power then the second power, over 2n factorial.

Maybe they didn't know what happens when you raise something to the zeroth power.

So if I tell you x to the zeroth power is equal to what, and I tell you that x is not equal to zero, what is x to the zeroth power?

Now any number other than zero to the zeroth power is going to be 1.

So i to the fourth is the same thing as i to the zeroth power.

We could make the arguement that zero to the zeroth power should be equal to one.

And the zeroth rule is don't panic. If you panic, you're never going to solve the problem.

So it becomes 4 times 5 to the first power, minus 2 times 5 to the zeroth power.

Actually, why don't you pause the video, and think a little bit about what zero to the zeroth power should be.

Five symmetries and then of course the zeroth symmetry where I just pick it up and leave it where it is.

Evaluate the expression 4n to the first power minus 2n to the zeroth power, for n equals 1 and n equals 5.

So that's where the definition or that's one of the intuitions behind why something to the zeroth power is equal to one.

If you take any non zero number and you raise it to the zeroth power, is we have already established that this is

But then there's a really good argument for why it should be 1, because any other number to the zeroth power is 1.

So this is going to be 4 times 1. Let me write it 4 times 1, minus 2 times 1 to the zeroth power.

And you could actually derive that even from this definition, but this is pretty straight forward anything to the zeroth power, including i is one.

All of the exponent rules are consistent with this definition of something to the zeroth power and this definition of something to the negative power.

5 to the first power is just going to be equal to 5. 5 to the zeroth power is just going to be equal to 1.

Hopefully, that gave you a little intuition as to why well, first of all, you know, the big mystery is, you know, something to the zeroth power, why does that equal one?

I exclude zero because zero to the zeroth power is usually undefined, or for our purposes you can accept it to be undefined and maybe in the future I'll do a video on explaining why its undefined, because it can either

Well, what I'm going to show you is one of the reasons, and then we'll see that this is a good definition, because once you learn the exponent rules, all of the other exponent rules stay consistent for negative exponents and when you raise something to the zeroth power.

Well, we could just keep doing this, and actually, we will keep doing this, and you know, just saying, well, the zeroth derivative, or at the value, is the same the first derivative is the same at 0, the second derivative is the same at 0, we'll say the third derivative, the fourth derivative, and we'll keep doing that.