Why do numbers to the power of 0 equal 1?

My attempt at making an instructional visual explanation. Music is by Eric Prydz.

[cakeandicecream]

It’s nice to see someone explain something simple in the most convoluted way possible. Usually teachers try to do the opposite, so it’s refreshing to see something a little different.

[esthersandoval]

Thank you so very much. This explanation is one that is so needed in order to understand this concept. If only middle school teachers would explain how to arrive at the answer of "one" when a number to the power of 0 is 1, then students would have logical procedures in arriving at an answer that makes sense instead of just repeating or memorizing that the answer is 1. Excellent. Loved the video.

[bahmannosratollah]

unbelievably easy explanation. easy to understand. Thank you.

[xNiGHT]

Not only that it was explained clear and concise, but It was also explained in a simple way, apart from what I've seen till now (and I have watched some videos in this particular subject). Love it, I am looking forward on this channel if I encounter another misconception. Thank you!

[garyfinch]

Thank you. Nobody has ever explained it so clearly and simply as you have, and for the reason that it has to be so. If they had, 40+ years ago, when I was at school, I might have had a more positive attitude to maths. As it wasn't explained to me, my attitude to maths, was akin to my attitude to religion; skeptical of anything that did not prove itself and was the only possible choice available. Thanks again, Gary.

[bradleystoll]

No one in the field of mathematics is debating whether 0^0 is 0 or 1. We are all sure that 0^0 is in fact not defined. Also, exponents are closely related to logarithms. In fact, in the history of mathematics you will find that logarithms have been around longer. Once one has defined the natural log function via the an integral (which is how many believe it should be done), then proving a^0 = 1 for all a > 0 is a trivial task.

[slimshadylife]

This was extremely helpful. I'm currently teaching myself Electrical Engineering and the book I'm using did not explain this and I was very confused. Thank you so much.

[RaaZVan]

I think an easier way to explain this would be this
a^x/a^y = a^(x-y) => a^(n-1) = a^n/a;

Let a=2 and let's start with 2^4 = 16;

2^4 = 16;
2^3 = 2^4/2 = 16/2 = 8;
2^2 = 2^3/2 = 8/2 = 4;
2^1 = 2^2/2 = 4/2 = 2;
2^0 = 2^1/2 = 1;


And moving forward, that's why 2^-1 = 2^0/2 = 1/2, etc;

[DigilusionStudios]

Sometimes you just need to find someone that can explain things in different ways to learn it, Thanks.

[mollymolster]

This was sooo helpful .I feel like sharing this with everyone I know but that would make me SERIOUSLY nerdy. lol.

[starpaw]

Thank you so much for this video, It was briefly talked about in my math glass but for me to understand something I need to know WHY, and this video explained it very well. Have a great day!

[BoahYo]

I was thinking about this and came to the same conclusion as the video. Just wanted confirmation

[mysticcyber]

Amazing!!!😅 This Video has single-handedly answered my lifetime's question or one of them, and my answer is that invisible 1 that no other video told me about. 😭Bravo *claps*

[cancionesdeyu]

0: OMG!!! I was stuck on this for so long! I FELT SO DUMB BUT THANK YOU SO MUCH FOR CLEARING IT OUT!!😭

[TheZmoliver]

Thank you! It's one of things I've always wondered about. It's like, you can go through entire courses and never have to know WHY it's this way (which usually means just taking someone's word for it). But I don't like to ever do that. I have to see it for myself. Thanks again!

[RealityCheckT]

I can't compliment your videos enough, they're wonderfully explained.

[zfgyywp]

Another way to prove that a^0=1:

a^n / a^n = 1 because anything divided by itself is 1.

But, if you apply one of your exponent rules...: a^n / a^n = a^(n-n)= a^0 = 1, because of the first line.

[indyjoe]

the breakdown at the end was excellent

[hello-ykhn]

Another way of proving it:

1
=64/64
=4^(3)/4^(3)
=4^(3-3)
=4^(0)

[buttermilkpancakes]

Omg thank you so much !!! 😭 this helped me out greatly.