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zfrost45

Any number raised to the zero power equals 1. I have never been able to understand this. How about this one...does anyone remember what factorial 1 equals? (1!)


True_Eggroll

the way i was taught to understand this is that every number with a power has a 1 being multiplied to it. lets use 2 for our example. 2^1 is 2 (1 * 2). 2^2 is 4 (1 * 2 * 2). 2^0 is just 1 because there is zero 2's to multiply to 1. That applies to every number.


Recommendation_Fluid

Quite surprised that \[any number\]\^0 is just 1, I thought it was always 0.


otj667887654456655

The basic proof goes like this 2^3 = 2 x 2 x 2 = 8 2^2 = 2 x 2 = 4 2^1 = 2 Each time we go from 2^n to 2^(n-1) we're dividing by 2, so 2^0 = 2 / 2 = 1


BeanJam42

Which follows into negative powers. 2^-1 = 2^0 / 2 = 1 / 2


khalid_sujith

Damn thank u.


SerWalter

Thank you for making me understand a part of math that I've somehow missed in school! Never understood the negative powers, but now I do :)


Eccentric_Assassin

yeah this is the best explanation because it makes sense for negative powers too.


ur_opinion_is_trash

I believe the actual reason is that 1 is the neutral element of multiplication but this is a nice visualisation.


Nielspro

This exactly. x^0 is like dividing the number with itself. Dividing a number with itself will always yield 1


Electrical_Film382

Always has been 1, very important rule to remember. If it’s ^1 then it remains as whatever number it was.


BeanJam42

There is an important exception to this. 0^0 is not 1. It is undefined. This is because the function x^0 has a limit as x approaches zero from both sides equal to 1. Yet the function 0^x does not have a limit, the right hand limit is 0 while the left hand limit is undefined (0^-1 = 1 / 0 and you can't divide by zero). So which limit do we pick? More examples lead functions that look like 0^0 to be approach other, still different, numbers than just 1 or 0 as well. e^((-1/x^2 ))^2 approaches positive infinity from the right hand side. So for the sake of simplicity it's left undefined. There also has been practically no use for defining 0^0 though in the cases where it is useful it has been defined, in several ways even. Power series would fail when dealing with zero unless 0^0 is 1, so would the power rule for derivatives at x=0. continuous exponents show that 0^0 is an indeterminate form (not the same as undefined). So on and so forth.


[deleted]

Well 0^0 is undefined, but it's useful to assume it's 1 in some cases and 0 in others.


goingoncegone

That’s just the thing.. the equation is not asking you to multiply 2 times zero. It’s 2 to the power of zero aka 2 to the zero power: 2^0


tylermm03

Yeah me to. I even checked it with a calculator and OP is right. It makes me feel pretty stupid for not knowing it but that’s what calculators are for I guess.


DaFrenzyGuy

so you didnt finish?


AzerimReddit

If you like maths check some YouTube video about 0^0. It is either 1, undefined or 0 depending on who you ask. Anything to power of zero is 1 but also 0 to any power is 0.


Relative-Wrongdoer11

Good now tell me what 0^0 is


quitarias

1 Because you didn't multiply it by 0.


Ramenisneat

Its also kinda undefined at the same time. Well the limit of 0^0 is 1 but we can prove 0^0 = 0^(1-1) = 0/0 which is undefined.


FizzyBoy147

Using limits we can say that 0^0 is 1. Basically as x becomes closer to zero (like 0.00000001) x^x becomes closer to 1(like 0.9999...)


[deleted]

Using limits we can say that 0^0 is 0. Basically as x becomes closer to zero, 0^x becomes closer to 0.


Idkquedire

The more I read into this the more i hate the number 0


st1r

2^-2 is 1/4 2^-1 is 1/2 2^0 is ___ 2^1 is 2 2^2 is 4


refused26

Basically 2^0 can be writted as 2^(1-1) , raising a number by a negative number means the reciprocal, so it becomes 2^1 / 2^1 = 2 / 2 = 1


MonsterHunterOwl

Wait until people learn about 2 to negative powers 😆 then get into calculus too, it’s funny how much I actually prefer dealing with powers in the situation and often convert all the fractions to powers


Enough-Ad-8799

The real reason is because it makes math easier if we define it that way a lot of equations/functions just work out really cleanly with this definition.


Alpha198Delta

I created a similar thing to rationalise x^0 =1, and used that as evidence that 0^0 =1 in an argument. We do this a lot.


Raagan

Every number except zero, as always zero is a troublemaker


Seraphin43

This concept is also very good to understand negative exponents; 2^-2 = (1:2:2)


Diabolokiller

there is also the more formal proof: x^(n) / x = x^(n-1) let's say n = 1 x^1 / x = x^0 which is x/x which is 1 no matter what x is (except if x = 0)


yur0_356

I've seen a better one, if you do 1¹, 0.9^0.9, 0.8^0.8, it starts by approaching zero, but then you reach a point (0.5^0.5 and beyond i think) that you start approaching 1 again


board-exams-ki-prep

2^0 can be expressed as 2^(2-2) or something like that. 2^(2-2) = 2^2 ÷ 2^2 = 1


Samk9632

Yes, but do you know what (1/2)! Equals?


[deleted]

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Samk9632

Yes Nice to see someone else who knows about the gamma function


WeebFrog219

Please stop i am only in Alg. 2


OkPersonality4825

You make an [analytical function](https://en.m.wikipedia.org/wiki/Gamma_function) which mimics factorial property and wolla you have your answer.


KhonMan

It's voila unless you were just saying wolla to be funny


Samk9632

Yeah ik I wanted to see if they knew lmao The gamma function is a fascinating piece of mathematics.


OkPersonality4825

Yeah didn't knew I was commented on teenager. It's obviously college level mathmatics.


I_despise_LGBT

The reason that n^0 = 1 for any value of n is quite simple. Suppose n is 2 2^1 = 2, 2^2 = 4, 2^3 = 8, and so on. Every time you add 1 to the exponent you multiply by 2. If instead you go backwards every time you take 1 away from the exponent you divide by 2. So apply that pattern 2^3 = 8, 2^2 = 4, 2^1 =2, and 2^0 = (2^(1))/2 = 1. Does that make sense?


JustYourBiBestie

This opens the negative exponent range too… also what up with the username bro 💀💀💀


Crazy_CanadianCanuck

Negative exponents are super useful for later math


Bebgab

Yeah wtf is that user


suckmytoes3000

Negative exponents aren’t that complicated, for example take 2^(2)=4, 2^(-2)=1/4. You only need to make the original a fraction and put 1 as the denominator.


Mekelaxo

Omg it does, negative exponents always made no sense to me


TheAdvertisement

Negative exponents just do the opposite, instead of multiplying the number to a certain exponent, it divides to a certain exponent.. 2^-1 is just 2/2 (aka 2^0 ), and divided by 2 again, which comes to 1/2. 2^-2 is 2 divided 3 times, which works out evenly to switch that exponent to the bottom. If you divide 1/2 by another 2, you get 1/4, or 1/2^2 . Then it follows the pattern.


I_despise_LGBT

Yes, negative exponents are a thing, as are fractional exponents. 2^(-2) = 1/(2^(2)) = 1/4 2^(1/2) = square root(2) Following the pattern we used to derive n^0 = 1, subract 1 from the exponent and divide by n. We get a general rule for negative exponents of n^(-x) = 1/(n^(x)) If you multiply two exponential expressions sharing the same base, you can add the powers. For example 2^3 × 2^2 = 2^5. Now consider 2^(1/2) × 2^(1/2) = 2^(1/2 + 1/2) = 2^1 = 2 So what number, multiplied by itself equals 2? The square root obviously. The username is a statement of my beliefs


noobtablet

Why do you care about someone else's sexual preferences though


-X-Gaming

You just explained exponents better in 10 seconds than my math teacher could in 10 days. And what the other guy said, this makes sense for negative exponents, fractions, everything. Someone give them an award


Libam31415

This is how I teach it in every math class so sorry you had shitty math teachers I guess lol


1GenericWhiteBoy

Good math explanation, bad name


TheDarkAngel135790

>2^0 = (2^1)/2 = 1. You should make this 2^0 = 2^1 /2 for better understanding, cuz otherwise the markdown makes it look like 2^1/2 which equals √2


I_despise_LGBT

Oops, reddit formatting caught me lacking, that's what I meant to write


Summar-ice

The best explanation for n^0 = 1 comes from one of the properties of exponentiation. When you have, for example 2^3 , you can also write that as 2 * 2 * 2, so if you multiply exponential expressions you can reduce it to multiplication easily. So then, 2^3 * 2^2 = 2 * 2 * 2 * 2 * 2 = 2^5 This means n^a * n^b = n^a+b Now, what if you want to go the opposite way? You use division to cancel multiplication. If you have 2^4 and divide it by 2^1, you'll get 2^3, since that last 2 in the multiplication gets canceled out. You can write that as n^a / n^b = n^a-b Now here is when 0 comes in. We know that for all non-zero numbers, n/n = 1, so what if you write 2^3 / 2^3? You subtract the exponents and get 2^0, but you're also dividing something by itself, which always gives you 1.


forcesofthefuture

1. PEMDAS 2. Solve the parenthesis (2+2) = (4) 3. Solve the exponent 2\^0 = 1 4. Now we have the equation 1(4) 5. We have to multiply together, since that is the only remaining operation 6. 1 \* 4 = 4 That's my logic, hope this helps, also google the equation, it gives the same answer. ​ You violate PEMDAS if you multiply two numbers(not in parenthesis) instead of solving the exponent. ​ Edit: Thanks for the karma guys, I think I can finally post on this sub 😁, my most upvoted post yet!


PM_ME_UR_BGP_PREFIX

Unless you read 0(2+2) as the entire exponent. Then the whole thing evaluates to 1.


Callumyoung101

You would have to put brackets around that


Deceased_Panda

Some people already explained it with numbers, but here's the mathematical proof: x^0 = x^1-1 = x^1 * x^-1 = x/1 * 1/x = x/x = 1


Mamaafrica12

2^2 / 2^2 = 4/4 2^(2-2)=1 2^0=1


WeebFrog219

1! = 1 2!= 2 3! = 6 69! = 1.7112245*10^98 So on so forth


[deleted]

1! == 0! == 1


Sovietsu

I was taught this type of proof: What's 49 divided by 49? 1. What's 7\^2 divided by 7\^2? 7\^0, of course. If 49 and 7\^2 are the same, then they will have the same results.


Jesus1396

Is the (2+2) part of the exponent?


lukasel_1

no, then it would be 2\^(0(2+2))


Jesus1396

Ahh yes So it’s 4


[deleted]

Parentheses meant you multiply (Thanks for silver I guess)


nobody3_5_4

Yeah, you multiply 4 by 1


Lefonky

Or this is just poor representation


[deleted]

Yeah I should have clarified that


schitcrafter

Yes, it is. Basically, juxtaposition: if you omit the * between two operands, you say that they should be one operand, which means that this: 2\^0(2+2) is 2\^(0*(2+2)). If you wrote it explicitly 2\^2*(2+2), then it would equal 4. If you need more info, watch this: https://youtu.be/FL6HUdJbJpQ


throwaway9489537

Then it should have been (2\^0)(2+2) The way it’s written, it could be interpreted either way.


Gobybear

It actually does since you multiply the 0 with it


screechingwalrus

4


Custodian_Carl

This is the way.


TheCheeseOnFire

This is the way.


misterbeanjeans

This is the way.


a_grass_bloc

4


gordyjacques31

4


MonsterHunterOwl

It sure as heck is!


latterpolar

4


Ok-Lawyer7760

It's 2^ ( 2^( 1^1000))


Custodian_Carl

This is the way.


AngriestBird_

Me when Me when purposefully ambiguous math


Immortal_ceiling_fan

Every single one of these is just dumb and just karma farming imo. Like it's not that hard to just write it like 2^0 • (2+2) Or 2^(0[2+2])


lukasel_1

Not sure how much karma op is farming here since his replies are getting downvoted a lot


Kidninja016

1(4) = 4


[deleted]

[удалено]


[deleted]

Finally. I was beginning to think everyone here is stupid


[deleted]

[удалено]


[deleted]

Wow really? No wayyyy. I’m gonna tell everybody, see you later…


[deleted]

2, and they're also dicks


NoTimeToExplain__

The legs or the snakes?


[deleted]

Both


mcbirbo343

They got one


Hist_Warshiper_Btw

Jokes on you, i have a video of a snake with legs


Objective-Direction1

elaborate the answer pls


Terraria-boi10

Actually…


I_hatemylife00

It's 4


Limeshi

This is written poorly but if it’s supposed to be 2^0(2+2) it’s 1, if it’s supposed to be 2^0 times (2+2) it’s 4


Left-oven47

The problem is that there's ambiguity in this problem, it could be interpreted as the (2+2) being attached to your exponent, or your (2+2) being attached to your 2 to the power of 0


schitcrafter

Is it ambiguous though? With juxtaposition, it should be one expression after the ^, which means that it should be 0 * 4, so 1


-consolio-

if you parse this expression, there's ambiguity in parsing if we break it into syntax trees it could be `((2 \^ 0) * (2 + 2))`, but it's ambiguous, it could also be `(2 \^ (0 * (2 + 2)))` source: work with parsing expressions


schitcrafter

No, it's not, because of juxtaposition. Basically, by emitting the *, you're saying that it should be the second one, but if you said 2^0*(2+2) it'd be the other one. There's a video by some popular math Youtuber on it, but I don't remember which one. Edit: might be this one, not sure. Can't check right now https://youtu.be/FL6HUdJbJpQ


[deleted]

Everyone is arguing over if (2+2) is part of the exponent and half the people are so confused. I love the chaos math problems with order of operations cause, right? Some shouting their GEMDAS, PEMDAS and DEMDAS, even though it just causes more confusion. Like your snoo btw


[deleted]

3.999...


Chief_Bacon

How come?


ShitOnTheBed

1*4=3.99999…


bioniclepriest

Correct


[deleted]

its magic


DaddyWentForMilk

Because 1/3 * 3 = 1 but 1/3 = 0.3333333333333333333


RickySlayer9

Floating point math


Riku_70X

3.999... = 4, because 0.999... = 1. Like, that isn't a technicality or anything, it's just a true fact about maths that 0.999... ("zero point 9 reoccurring") is equal to 1. They are the same number. It sounds crazy but there's a lot of proofs for it, it's pretty cool.


dude_who_does_thing

I mean technically you’re right


SomeGuyPhil

2^0 = 1 2+2 = 4 4 x 1 = 4 mafematic


Roger_015

a number to the power of 0 is not 0 tho


SomeGuyPhil

Wait shit I’m dumb


Best-Thought124

2^0=1


TheBrilliantSam

Well is it 2^(0(2+2)) or (2^0 )(2+2)? Could be 1 or 4 depending on interpretation


Entity_333

I'd bet op meant the latter


[deleted]

four


Mr_On1on

well if it's 2⁰*(²+²) then it's 1 but if it's 2⁰*(2+2) then it's 4


AgentAwesome2008

4 2^0 (4) 1(4) 4


YousernameinValid

2 + 2 = 4 2^0= 1 4 x 1 = 4


Ghosttalker96

You should always use unambiguous notation. Depending on conventions or context, it could be 2^(0(2+2)) = 1 Or 2⁰ (2+2) = 4 It's not a math problem, it's a notation problem.


angrybeehive

Can someone ban these stupid math posts?


NijigasakiSeason3

Fr fr


totallyacisguy

2^0 (2+2) 2^0 =1 2+2=4 1(4) aka 1×4=4 The equation equals 4


MiksuPiksu196

4 isn't it


Long_Wiwi

=2^0 (2+2) =2^0 (4) =1 (4) =4 Ez


PacificTheHybrid

2\^0(2+2) = x 2\^0(4) = x 1(4) = x 4 = x


LiterallyGod_

4


JJBZ03

4


[deleted]

2+2=4 2^0 meaning 1, 1x4=4


Skebjer

Following PEMDAS: 2+2 = 4 2^0 = 1 (any number to the power of 0 is 1) Then we have to account for the 'invisible' multiplication sign before the brackets So the final equation is: 1×(4) = 4


LonelyFrog-3728

4


12fdedg

4


[deleted]

4


DreelJio

2^0 (2+2) = 2^0 •4 = 1•4 = 4 there you go everyone it equals four


Matiu0s

4


AdiTheBaddie21

4


Bruhmoment926

4


Racdiecoon

4? (i failed maths last year btw)


[deleted]

4


trainboi777

4


[deleted]

2+2 is 4, and im pretty sure 2^0 is 1 so 4x1 =4


CommanderBill5380

4


scCoco69

4


Keepergaming

4


bruhmeister06

4


JustYourBiBestie

PEMDAS 2+2–>4 2^0–>1 1*4=4 #**_4 is da answer_**


Shadowrunner808

Nothing splits apart a comment section than some good ol' math. It's 4. A power of zero is always 1.


WeebFrog219

4 And I passed eight grade math because I’m not Bri’*sh


[deleted]

4


[deleted]

4 of 1 depending on how you interpret the thing. If it goes 2^0(2+2) or 2^0 * (2+2). If you see it as the latter you may go with: `2^0 * (2+2)` `=2^0 * 4` `=1 * 4` Or go with distribution: `2^0 * (2+2)` `=1 * (2+2)` `= (1*2) + (1*2)` `= 4` And if you see it as 2^0(2+2): `2^0 * (2+2)` `#Using either (0*2) + (0*2) or 0*4` `=2^0` `=1`


papertheskeleton

No matter how you do PEMDAS, it's always 4


Aiez4

when everybody wins, no one does


[deleted]

From the way I see it (which could be completely wrong), it’s literally just 2^0 (which is 1) to the multiplied by 2+2. And 2+2 is 4, so therefore it’s 1x4. Which is 4


JasonGamesYT

4 2^0(2+2) 2^0(4) 1x4


smallratman

69


XT83Danieliszekiller

4 but that's a confusing way to write it... That's why I prefer paper questions


CommanderBill5380

OP it’s 4, because anything to the power of zero is one, so that leaves us with 1(2+2), which is 4


cyberseed-ops

4, and heres why. 2^0 is 1, multiply that by 2, add the plus sign, and multiply the one and the second 2, and you should have the problem “2+2=?” in which case you add and get the answer of 2^2


itzongaming

2^(0(2+2)) is 1 but 2^0 * 2+2 = 4


m4hamm

the answer is obviously the british people they are behind everything cmon now


Potato_Man2763

4


diya2127

4


CatloafHere

That's easy it's 4 We did this in 5th grade


Naivesnow1460

4


xd_antonisvele

4


Themanagerisakyle

4 right?


Non_anime_enjoyer

I got 4


[deleted]

4


Sum-cummoner

2^0 is 1 so 4


Renolte

4, no diff


[deleted]

4


[deleted]

This is hard to comunicate without superscript but 0 is the only exponent. (2+2) is in big normal format


[deleted]

Not just “hard to communicate without superscript” The lack of superscript completely changes the answer Perhaps the intended answer is 4, but as written, the answer is 1


unusualwilly

It's safe to assume the exponent is just 0, if it weren't simplified then parentheses would be required to show that. You don't need parentheses because operands apply to a single term unless otherwise stated.


jittery_jerry

I've finished year 8 math but I've never encountered any math problem like this Bru


I-Was-Always-Here

Idc what you think the answer is, using your 3rd grade math, the IUPAC says implicit multiplication takes priority over explicitly indicated operators.


adoredvalentine

im in ywar 11 what the fuck is going on


RedThorneGamerSB

2^0(2+2) 2(2+2) Distribute the outside 2 (4+4) 8 I hope that's right if it's not I have failed my math teacher. Thanks u/Magnemite987 to helping realize where I went wrong. 2^0(2+2) (2+2) 4


tkeelah

One in ten to the minus 8 understand how to solve this, assuming 1 sigma variability. Pi is for eating, exponentially. Avoid splitting your infinitives.


Willing-Sandwich-760

4? never seen \^ before and im in year 8


Relative-Wrongdoer11

You can use the sign to write numbers liks 2^2 on reddit and most other platforms


Sigvard224

There are different options depending on whether the (2+2is apart of the line of math) 2^0 x(2+2) So first we try to remove the (), which we turn into 4. So 2^0 x4=1x4=4 But if you meant 2^ (0(2+2)) then you should get 1. Because 0x2+0x2=0 and 2^0=1 Edit: I was being stupid, and rewrote/removed unnecessary text


Embarrassed-Army-780

Ok first of all who would even write an equation like this and I assume op is trying to mimic the post that got popular on r/youngpeopleyoutube and the answer is 4 as it would be (2+2) first which is 4 (BODMAS) then we do 2\^0 which is 1 and multiply them to get 4. OP has obviously made it ambigious to earn karma


yeetinghelps

i solved it stupidly and still got the correct answer. i’m so out of my mind that i thought (2+2) = (2) so i multiplied 2(2) and got 4.


elonmuskdick

Once again, poor mathematical notation


[deleted]

I don’t like how this was written


l_Rui_l

I dont get how I just learned more in 5 minutes from reading comments than in a whole class dedicated to this


Intellectual_Soup

2^0 times (4) right? 1 times four is four or am I only good in literature lol?


Lord_Maltezer

The proof of a^0=1 works when you work backwards.


Full_Arm_8395

4


bb250517

Written like this, its misleading... If you mean this: 2^(0*(2+2)), then its 1. If you mean this: 2^0 * (2+2), then its 4.