*Thanks for explaining why* the zeroth power is equal to 1. When I was taught this, and exposed many times since, over 50 years ago, teachers just said _remember any number to the zero power is 1._
Salman, I truly look up to you for your determination to educate people on math. I know that you have truly educated me. With no money being placed in your pocket, you still help students all over the world with math. A man who does something good for people and receives no pay is a good man. Please continue your good work :)
"Powers of two are always very interesting. It's specially interesting if you one day go into computer science." well you are right Sal!(like always!) for I have memorized powers of two up till 65536! Sheesh! And I love computers!
Wow Khan. It looks like you're developing a fan base. I'm watching these vids as a brush up for a state exam that will have math on it. So far it is helping my brain prep for my big day.
hey, man thanks, im usually the one to put magic on youtube, but im homeschooled, and needing a big help with exponents, thanks 2 u, im getting it now!
Actually, no! 0^0 is what's called an INDETERMINATE FORM, an expression that does NOT have a fixed, known value. 0/0 and infinity divided by itself, as well as 0 times infinity are other examples of indeterminates. You'll see this in calculus, as well as how to deal with functions that produce them.
Um obviously you need a life.And if you think math in general is boring your probably not gonna get a life.He's doing a wonderful job of teaching people math!
omg i tried doing the exponents lvl 1 modgule and i couldnt get it and then i watched the vid and i got all of them right . luv u salman !!!!!!!!!! ur a living miracule !!
@cnuts83 the order of operations (OOO) is what's important here. remember that exponents are done after parentheses and before multiplication in the OOO. so when we're faced with -3^3, the exponent is calculated first, so 3^3 = 3 * 3 * 3 = 27, and then the negative sign is considered (a negative sign is the same thing as multiplying by -1), so -3^3 = -27. for (-3)^3, parentheses come before exponent in OOO, so (-3) * (-3) * (-3) = - 27.
Just would like to say everything Mr Steroids said and more. Nobody ever explained why anything to the zero power was one, I always for got this as I didn't know why the answer is one for any number. Now I actually understand this and no longer have to memorize it. You are such a legend. Do you have any videos on FOURIER SERIES? thanks again for thee knowledge. If I make a carrier in life its thanks to you and I will donate what I can.
well 2^3 = 2 x 2 x 2 = (2 x 2) x 2 or 2 x (2 x 2) = 4 x 2 or 2 x 4 = 8. Remember when multiplying, it doesn't matter which side you start from. so it doesn't matter if you have 2 x 3 x 2, if you start from the middle (3 x 2) you'll get 6. then you'll have 2 x 6 = 12. so in simpler forms - 2^3 = 2 x 2 x 2 = 4 x 2 = 8. Good luck.
@prence1725 sometimes parentheses are used for emphasis. saying 2 * 3 + 2 is saying exactly the same thing as (2 * 3) + 2, so the parentheses are only there for emphasizing the fact that you do 2 * 3 first and + 2 second.
1:26 yeah that's my Achilles heel. Also the order of operations. Multiplying, dividing, Adding and Subtracting is easy. The mobile game Yu-Gi-Oh Duel Links helped me with adding and subtracting on high decimal numbers. So these smaller numbers aren't that hard.
Yes. -1^1000 is -1 since the negative sign is not part of what you raise to the 1000nth power! :) So, -1^1000 is the same as -(1)^1000. But when you include the negative sign: (-1)^1000, you have to know whether the exponent is an even number or an odd number. Am I late in my reply? Maybe you've already learned this.. Hope it helps in any case! :)
I believe you are correct, as per the order of operations. I notice he usually puts the negative value in parentheses with the base value. This would change the calculation. I just saw this yesterday. I see that your comment is 14 years old.
X/0 = "undefined" and 0 to the power of 0 = 0^0 = "undefined". So X/0 = 0^0 => X = 0^0 x 0 = 0^1 = 0 which means that "undefined" = 0 Problem solved! (If you think this is just a really bad joke, you would be right ;-)
What about something like: (-3²)? I've been told that having the exponent on the inside of the brackets make a big difference to what the answer is? How does that work? Also, yes I am a video game character asking mathimatical questions. DEAL WITH IT! :P
Could you explain the differences between these examples, -3^3, (-3)^3, (-3^3), -(3^3). It boggles my mind that the differences between where the parenthesis are placed would change the rules. I don't understand why the sign would be carried along with some and just added automatically depending.
Please Excuse My Dear Aunt Sally is a thing we learned too :-). And then, my sixth grade teacher said that she wanted us to forget that and follow P E M&D A&S because sometimes when people head straight for the parentheses they do addition or subtraction before actually multiplying and dividing. Just some pointers for 6th Grade I'd thought I'd share :-).
the irony of the khan videos - they are so clear, yet... if you did a word count of every single khan video, the most frequently used word by far is "confused"
could another explanation for anything to the 0th power be this. x^n/x^y= x^n-y, therefore x^n/x^n be 1 because any number divided by itself is one right?
exponents are the same as addition is to multiplication sorry I probably confused you. No sir you did not lol. in fact I'm here to tell that after you said that I didn't need to watch the rest of the video and you're a great teacher. (I did watch I anyway just to make sure I miss anything)
On a + - graph; applying it to real life situations. Lets see; if I have not 4 apples I can write it as negative - 4 apples. If I have another not 4 apples or - 4 apples; how is it I don't have - 8 apples; instead mathematically I have plus + 8 apples. How is this, someone please explain?
***** No, -1^10 = -1. -1^10 means -(1^10), which is -1. If you want the negative sign to be included when you're taking powers, then you need the brackets: (-1)^10 = 1. However, Sal acknowledged his mistake in the video. In general, (-1)^n = 1 if n is even, and -1 if n is odd.
*Thanks for explaining why* the zeroth power is equal to 1.
When I was taught this, and exposed many times since, over 50 years ago, teachers just said _remember any number to the zero power is 1._
I really had hard time to figured out that why is any number to the zero power is 1 but this video helped me a lot. Thank you.
teachers should be fired. This guy should be paid
Respect
Salman,
I truly look up to you for your determination to educate people on math.
I know that you have truly educated me.
With no money being placed in your pocket, you still help students all
over the world with math.
A man who does something good for people and receives no pay is a
good man.
Please continue your good work :)
"Powers of two are always very interesting. It's specially interesting if you one day go into computer science."
well you are right Sal!(like always!) for I have memorized powers of two up till 65536! Sheesh! And I love computers!
KHAAAAAAAAAAAAAAN!!!!!!!!!!!!!!!!
Devon Taylor I am so glad introduced me to this!
this makes so much more sense then when my teacher was teaching this! :D THANK YOU KHAN ACADEMY!! :)
What are you using on your computer? I want to use the all black board with computer mouse drawing to
yup same here !
Ameen !!
mashallah we need more ppl like him in the world :-)
This video came out before I was born 😅who would have thought it'd be my lifesaver Thank you Khan Academy🙏
DUDE !!!i love you and the way you teach
taking the GRE in about a week and you just cut my study time almost in half
thanks for the little blip on why 3 to the zero power is 1!!! it makes sense!!!
I’ve been falling behind in math and this is the only thing that helps!
I think it might be useful to explain why you use parentheses around negative numbers, and what happens when you don't use them. :)
The ^0 explanation was superb. I never really did learn about that from any of my math teachers.. thanks.
i find it amazing he chose educating kids over millions of dollars.
this makes a good man
This is my first year homeschooling, and I'm in 7th grade. I was really confused so my mom made me watch this. IT WORKED!!!!
Good bless you sir. I have learned a lot from your videos.
i learned about these videos because khan academy was referenced in dylan rattigans book and the actuality lives up to the hype i must say
Wow Khan. It looks like you're developing a fan base. I'm watching these vids as a brush up for a state exam that will have math on it. So far it is helping my brain prep for my big day.
this guy is the best math teacher on the planet
hey, man thanks, im usually the one to put magic on youtube, but im homeschooled, and needing a big help with exponents, thanks 2 u, im getting it now!
Actually, no! 0^0 is what's called an INDETERMINATE FORM, an expression that does NOT have a fixed, known value. 0/0 and infinity divided by itself, as well as 0 times infinity are other examples of indeterminates. You'll see this in calculus, as well as how to deal with functions that produce them.
Nine years later but very interesting :)
Thank you so much this will help me get in to algebra 1
Um obviously you need a life.And if you think math in general is boring your probably not gonna get a life.He's doing a wonderful job of teaching people math!
omg i tried doing the exponents lvl 1 modgule and i couldnt get it and then i watched the vid and i got all of them right .
luv u salman !!!!!!!!!! ur a living miracule !!
@cnuts83 the order of operations (OOO) is what's important here. remember that exponents are done after parentheses and before multiplication in the OOO. so when we're faced with -3^3, the exponent is calculated first, so 3^3 = 3 * 3 * 3 = 27, and then the negative sign is considered (a negative sign is the same thing as multiplying by -1), so -3^3 = -27. for (-3)^3, parentheses come before exponent in OOO, so (-3) * (-3) * (-3) = - 27.
thank you for these videos. going to help me get ot college level math (:
This seems stupid
Zanna Ravin All math is stupid, just go with it.
Just would like to say everything Mr Steroids said and more. Nobody ever explained why anything to the zero power was one, I always for got this as I didn't know why the answer is one for any number. Now I actually understand this and no longer have to memorize it. You are such a legend. Do you have any videos on FOURIER SERIES? thanks again for thee knowledge. If I make a carrier in life its thanks to you and I will donate what I can.
one of the first videos of khan academy!
I LOVE YOU KHAN, YOU'RE AMAZING!
Thank you for all this help,you give us!
omg..my students multiply them constantly too..I will try teaching it this way right next to each other..thanks!
I Hate maths and i never understood exponents until i watched this vid! thank u so much!!!!!!!
well 2^3 = 2 x 2 x 2 = (2 x 2) x 2 or 2 x (2 x 2) = 4 x 2 or 2 x 4 = 8.
Remember when multiplying, it doesn't matter which side you start from. so it doesn't matter if you have 2 x 3 x 2, if you start from the middle (3 x 2) you'll get 6. then you'll have 2 x 6 = 12.
so in simpler forms - 2^3 = 2 x 2 x 2 = 4 x 2 = 8.
Good luck.
@prence1725 sometimes parentheses are used for emphasis. saying 2 * 3 + 2 is saying exactly the same thing as (2 * 3) + 2, so the parentheses are only there for emphasizing the fact that you do 2 * 3 first and + 2 second.
@EGMAG It more or less applies to square feet. If your a contractor or a fence builder you would use it and other proffesions like that.
1:26 yeah that's my Achilles heel. Also the order of operations. Multiplying, dividing, Adding and Subtracting is easy. The mobile game Yu-Gi-Oh Duel Links helped me with adding and subtracting on high decimal numbers. So these smaller numbers aren't that hard.
ok the -1 part helped the most i never new that!
I was stuck and could not figure out where i was going wrong. then you said rem. x not add.. DUHH!! AND MY ANSWERS ARE NOW CORRECT!! THANKS YOU kHAN!
The like bar looks like a green pencil.
education is a powerful thing known for its miraculous healing powers of the self esteem .
Yes.
-1^1000 is -1 since the negative sign is not part of what you raise to the 1000nth power! :)
So, -1^1000 is the same as -(1)^1000.
But when you include the negative sign:
(-1)^1000, you have to know whether the exponent is an even number or an odd number. Am I late in my reply? Maybe you've already learned this.. Hope it helps in any case! :)
I believe you are correct, as per the order of operations. I notice he usually puts the negative value in parentheses with the base value. This would change the calculation. I just saw this yesterday. I see that your comment is 14 years old.
5:14 that power to 3 looks like a face lol :) 😂
Suneel Nadipalli xcxcccfxxxdxxz
@colombianchic128 you square the 8 and the 9. so 8 * 8 = 64, and 9 * 9 = 81. so the numerator is 64, denominator 81.
So, I am doing the same level of math as my 5th grader, and I would like to say a heartfelt "thanks!" I think I'll pass that DMA -10 exam on Monday.
My mathbook could never teach me this well... no kidding! :)
This is alot better and understandable!!!
Thank you so much for your videos, they help me so much and you explain everything so well
I have question you said that anything to the power of 0 = 1 but wouldn't 0 to the power of 0
still be 0 please tell me if this is correct
Great really helpful!!!!!
agreed
Thank you for a very informative and easy to understand math lesson!
Wow so good
X/0 = "undefined" and 0 to the power of 0 = 0^0 = "undefined". So X/0 = 0^0 => X = 0^0 x 0 = 0^1 = 0 which means that "undefined" = 0
Problem solved!
(If you think this is just a really bad joke, you would be right ;-)
What about something like: (-3²)? I've been told that having the exponent on the inside of the brackets make a big difference to what the answer is? How does that work?
Also, yes I am a video game character asking mathimatical questions. DEAL WITH IT! :P
Thanks.
4:45 is true for all bases except when the base is 0. that's the only exception.
This helped me learn more. In school about order of operations video pemdas this is what I know
Could you explain the differences between these examples, -3^3, (-3)^3, (-3^3), -(3^3). It boggles my mind that the differences between where the parenthesis are placed would change the rules. I don't understand why the sign would be carried along with some and just added automatically depending.
Thanks. We are learning this in school in 4th grade. Also decimals.
Very helpful video. Thanks so much :)
I usually get the temptation Mr.Khan was talking about in school
e.g 3 to the second power equals 6 which would be wrong
Your videos are really helpful!!
We are learning the please excuse my dear aunt sally thing in 4th grade.
ahhh, cool :)
Yurushimo Kagayatake I did that too!
Nicole Weebot By the way i mean when i was younger!
Nicole Weebot im 12 by the way, i said that the wrong way.
Please Excuse My Dear Aunt Sally is a thing we learned too :-). And then, my sixth grade teacher said that she wanted us to forget that and follow P E M&D A&S because sometimes when people head straight for the parentheses they do addition or subtraction before actually multiplying and dividing. Just some pointers for 6th Grade I'd thought I'd share :-).
Super compressive. Engaging format.
it equals one listen to him carefully and to support this statement : (1-1)o = 0o (consider the o as 0 exponent).
People saying this is getting them though college level math:
Me who’s in seventh grade: *visible panic*
This is the best way to learn math
You are the best
this guy is genious..
2^3 = 2x2x2=8 the 2's represent the exponet which is three. so multiply 2, 3times
@prence1725 Very much. I don't remember what property or whatever it is but it's saying you do that part first of something like that.
the irony of the khan videos - they are so clear, yet... if you did a word count of every single khan video, the most frequently used word by far is "confused"
I'm going back to school after over 15 years and needed a refresher badly. I must say.........I LOVE YOUR VIDS. Thx champ!!
you should talk about if sci-fi could really happen.
your question is very vague. Please expand what you mean by sci-fi since it can encompass most fake and real technologies
Bruh I’m really in highschool picking up on the slack from my math teachers
Why did you nested parentheses in every negative number
so where are these moduals he talks about? Ive gone to his site but cant see them :S
@assadullahch I m also from Pakistan. Preparing for my O Level 9th grade exam! Ameen from me too.
Isn't -1^1000 = -1 as per the order of operations?
Thanks for the tips, even though im in 5th grade and already know about them. Thanks anyway :)
could another explanation for anything to the 0th power be this.
x^n/x^y= x^n-y, therefore x^n/x^n be 1 because any number divided by itself is one right?
jonjonjon1370 yes. Absolutely correct
Clever
Khan>>>>> every teacher I ever had.
(8/9)^2
=
8^2/9^2
=
64/81
Hope that helped! :)
1000th like
Sal is Genius
thanks bro im in 2020
I learned this last year they are easy
exponents are the same as addition is to multiplication sorry I probably confused you. No sir you did not lol. in fact I'm here to tell that after you said that I didn't need to watch the rest of the video and you're a great teacher. (I did watch I anyway just to make sure I miss anything)
How do you solve this problem
25+2^4 - 13 *2= 31
follow PEMDAS
Thanks a million...
Is there a difference between -3squared and (-3squared) ?
No.
no but there is a difference between -3squared and (-3)squared
On a + - graph; applying it to real life situations.
Lets see; if I have not 4 apples I can write it as negative - 4 apples. If I have another not 4 apples or - 4 apples; how is it I don't have - 8 apples; instead mathematically I have plus + 8 apples. How is this, someone please explain?
It's been 13 years since you asked and I have the same doubt now.
Did you find your answer?
I dont understand
what do u mean 'wtf' this guy is a fucking beast
Ok it would be 1 over w/e ur number is. For example
3to the power of -3 would be 1/ 27.
This helped me a little. Thanks!
-1^1000 = -1 NOT 1. The 1000 is not on the negative.
+Matt Haugen Correct. However, he appears to have acknowledged his mistake in the video (he put an annotation on-screen).
*****
No, -1^10 = -1. -1^10 means -(1^10), which is -1. If you want the negative sign to be included when you're taking powers, then you need the brackets: (-1)^10 = 1. However, Sal acknowledged his mistake in the video.
In general, (-1)^n = 1 if n is even, and -1 if n is odd.
Umm... What grade is this for?
what happen if the exponents is negative what i do???
help meeeeee
thank you
Jesus luvs y’all!❤️✝️❤️ just a reminder!