ZERO POWER RULE EXPLAINED + what is zero to the zero power? | Math Hacks

warm-up exponent example » 1:15
why any non-zero number to the zero power equals 1 » 2:32
what is zero to the zero power equal to? » 3:53

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#algebra #exponents

[سفيانآلعيسى-حض]

Haha.. 2 programing languages and even OS but i never noticed that 2^0=1 and why, now i feel like a little boy going to school*.*
you did great, thank you.

[MyKombucha]

Discovering your channel, here. Thank you for initiating that, for the quality of videos and your obvious love of teaching :) I've been looking to revisit the basics to be more confident and just take out the trauma of math altogether, lol.

[voidisyinyangvoidisyinyang]

I would recommend studying Alain Connes' lecture of "Music of the Spheres" and how since exponentiation is noncommutative, therefore a number to the power of zero implies a noncommutative inversion of the number (including 1 itself). So in music theory 2/3 is C to F while 3/2 is G to C. Therefore to claim that 3 to the 0/2 to the 0 = 1 is a commutative lie about the truth of reality. Thanks for clarifying this noncommutative point more dense than the real numbers that Connes calls, (2, 3, infinity).

[animeshjaiswal]

Loved the way you present the concepts and make watching and learning maths so easy and interesting.

[FillerWorld]

Oh, God! You deserve much more subscribers! Great content and explanations!

[AlbertTheGamer-gksn]

0^0 comes to a problem of being undefined due to the arithmetic-geometric transfer. In the arithmetic-geometric transfer, all 0's become 1's and the operation hierarchy moves up by 1 level: Addition to multiplication, multiplication to exponentation, and exponentation to tetration. Therefore, 0^0=1^^1, or 1 tetrated to 1. However, 1 tetrated to 1 is just a power tower of one 1, so if 0^0 is undefined, 1 tetrated to 1 is also indeterminate, and all real and complex numbers are UNDEFINED! Also, 0 factorial has the same discrepancy as we know that factorials of nonnegative numbers is the product of all numbers less than or equal to the number. Since 0 is an annihilator, 0 isn't included in the product. Therefore, 1 is the lowest number that can use the factorial definition. However, we know that (-1)! is infinity, so 0!=(-1!)*0 (due to the factorial rules), but that is infinity*0, which is also undefined. Therefore, 0^0 and 0! live and die together: If 0! is 1, 0^0 is also 1, and if 0^0 is undefined, 0! is also undefined.

[pcybvik]

I was looking for something to explain hexadecimals and why 16^0 is 1and this was perfectly explained, thank you! I love the notebook, pens and nails. Makes the whole thing less intimidating as I really struggled with maths in school

[TrilokNegi]

It is very helpful to understand and clear my math concepts. I liked this simplistic approach the math problems are explained and solved. Thank you Brett.

[GospodinJean]

WOW. IF I HAD A TEACHER LIKE THAT, I Would be both In love AND certainly been better in math!

[SanjayShelat]

Thanks for the video - that was a really good explanation!

[vorpal]

* Indeterminate, and not indeterminent. Intdererminent isn't a word.

[jonminer]

The discrepancy occurs because of the fact that we are using shorthand to do math. For most of human history, there was no zero. They either had something or they didn't. They did not think that they had zero sheep. They had no sheep. Two times two is the same as having two pairs. If we are sharing the income from selling sheep, and we sell no sheep, we do not share half of nothing. Even if we have twice as much we still share nothing. We have learned to use shorthand to compute complex problems. Zero should not be allowed as an exponent. In old ages, when there was nothing they left a blank. That is what we should do with exponents. If two exist in reality, then two being multiplied by nothing is two. Seems like a major problem for math. But multiplication and division are simply adding and subtracting in shorthand. Reality exists in one dimension and math in another. The answers we get in math depend on the rules we use for solving problems. There were several orders for solving problems which use parenthesis, right? Computers would solve left to right. They would get wrong answers and had to be instructed on how to solve which parts of a problem first.

[osazeeosarenmwinda]

Hi, that was a very great video you posted. It really helped clarify the wrong thoughts of one of my psychotic students perception. He likes to call himself GIGATOKONI. However please can I know the name o that 0.5mm pointed pen that you used in the video. It looked so porsche and I would like to get one for myself. Please reply when you get this feedback.

[matthewhowey]

Hi liked the way you explained the problems with division by zero. However earlier you demonstrate the property x^(n-m) = x^n/x^m using natural numbers, and then go on to say it holds for all Nonzero real numbers. I don't think that's valid reasoning, you've only demonstrated it for natural numbers

[asolutioncompanylimited]

awesome background even better explanation.

[presidentgateway]

At one point, she writes 2^1 / 2^1 = 2^0. But she gets that only by doing the shortcut of subtracting the exponents. 2^(1-1) = 2^0. But that's a shortcut. Doing the long form, the exponent zero doesn't arise. That doesn't seem satisfying.

Saying that anything divided by itself is the same as raising that number to exponent zero seems like just making a definition that delivers the proof desired.

[ben_w]

Pretty good, but a couple quibbles: I don't think you emphasized enough that these are just *motivations* for defining things as we do. But we could have defined things differently if we had so desired, and no 'proof' could prevent us. Also, 0/0 is undefined, not indeterminate (and certainly not indeterminant!). You seem to be thinking of the indeterminate form of a limit, which is not the same thing as simply dividing zero by itself. But yeah those are just quibbles. Nice video!

[reginakazanjian]

I love your videos! Thank you so much for explaining concepts in a way I really get. :)

[caminoOSRS]

Maybe i'm just missing something but with that formula you are just proving that 1^0 = 1 because alle numbers devided by themselves equal 1. But what if you want to do 2^0? Wouldn't you get 2^1/1^1 and as a result get 2^0 = 2?

[justabunga]

0^0 is indeterminate. This is useful in calculus when you compute limits of 7 indeterminate forms using l’Hopital’s rule.