Negative Exponent Intuition

[AdielG19]

my teacher said it would require too much math to explain this..wow if she knew it was this easy! great job!

[MissJayster]

thanks!

[lucache95]

thank you very much! i was frustrated because i didnt understand. i do now :)

[kindergartencow]

Thank you! Your videos are helping my GRE studying immensely! :)

[paulceltics]

no one can dislike this :)

[Liaomiao]

I'm 27, learned up to vector calculus with the help of your videos as well as some other free online lectures, and have all intentions of pursuing mathematics further in my spare time. I never understood what negative exponents were intuitively until now. Can't believe I didn't figure this out on my own. I'm both very embarrassed and very grateful. Thank you.

[ryujj143]

thanks for explaining this...it makes sense now

[ihasacarify]

good vid really helped

[VIR092]

Ah! The Dazzling....

[falconfanelite]

can anyone please help me with my algebra 2!!! please!!! its a online course and if i pass it i can graduate! please i need help with my algebbra 2

[MariusFlaubert]

Uh... What is he trying to say with "intuition"? Sorry, English is not my native language so I really don't understand...

[AnimesAreCool123]

No offense man ur good at teaching but i bet u 100% we dun need all this in real life so why are they even teaching us all these confusing bs... all we need in real life is to know simple addition, subtraction, multiplication, and division....AND YET THEY ARE FORCING ALL THESE CRAP INTO OUR BRAINS

[xXxEmogal999xXx]

@AnimesAreCool123 you think hes filling u with bs, but based on your comment u r already full of it...

[AnimesAreCool123]

@xXxEmogal999xXx First of all u gotta stfu u dun even no wat im talking about....Pls reread the comment again u noob...

[xXxEmogal999xXx]

@AnimesAreCool123 what changing your opinion? looser...get a life and dont spend it hatin on math videos that you dont even have to watch. And im pretty sure your first comment came through clearly to me... unless of course you want to elaborate...?

[AnimesAreCool123]

@xXxEmogal999xXx Omg u still dun get my point wat im trying to say is that even though we really dun need all these math in our lives we still have to learn them and i still have to learn that is why im watching these vids so i can get more knowledge....

[lovexlaine]

khanacademy = love.

[GenericCoder]

Thank you for your amazing Contribution to the world.I have been learning a lot from your videos and developed a really good interests for math.

[lexinaut]

Nicely explained! The Sand Reckoner (Archimedes) who may have been the first human to explore exponents systematically would approve, I think. May the pure beauty of logic aid purging our societies of their excessively greedy and violent tendencies. Math is indeed beautiful!

[atlanta5321]

this was amazing. i completely understand something i thought i would never understand. ty

[josenros]

I love understanding where these math conventions come from.

[EvanYM]

Thanks =D

[FarrenfollowsBen]

THank you ~!!!

[amoxtlacatl]

HELP HELP HELP

Dear Salman:

Your intuition is brilliant! I love it. Thank you!

But I have a question.

1) Division by zero is supposed to be undefined - or equal to infinity. Are both of these statements right - or if only one is right, which one is it?

2) Regardless, ANY NUMBER TO THE ZEROTH POWER EQUALS ONE, including 0^0 = 1. If I follow your intuition, that would mean 0/0=1. Does this not violate division by zero?

I don't mean to bother you - I am honestly curious.

Again, thank you.

[amoxtlacatl]

@amoxtlacatl

In found the answer elsewhere.

For those interested, you can read it by googling:

"sci math FAQ: What is 0^0?"

Still, it would be nice if Salman did a video explaining this.

[atlanta5321]

@amoxtlacatl i think 0^0=0/0= undefined

[lexinaut]

@atlanta5321 It is undefined, and in Calculus is called an "indeterminate form." It is worth slowing down and thinking about what 0/0 is. What a strange idea! DIVIDING NOTHING BY NOTHING! HOW MANY NOTHINGS FIT INTO NOTHING? Is this infinity? If so, infinity is NOT a number. It's more like a destination you can't reach. What do you think?

[lexinaut]

@atlanta5321  You can also make the argument that 0/0 =1, but that doesn't work mathematically for many reasons. If something might equal 1 or infinity, we might want to say it is indeterminate!

[amoxtlacatl]

@amoxtlacatl

Dear Salman:

I found the answer elsewhere. Thanks anyway. :)

For those interested, you can find it by googling:

"sci math FAQ: What is 0^0?"

Still, it would be nice if Salman did a video about it.

[Garmezan]

algebra sucks!....and this dude wants to play the teacher that maybe he dreams to be in real life.

[MrRasgabriel]

@Garmezan Dont hate dude... 

[eloexplorer]

@Garmezan

this person has helped many people way more than teachers in real life. he is just brilliant.

[Pogueconductor]

this one was so much louder!

[LostCivilization]

Not sure if this was covered elsewhere. But some calculators give wrong answers when inputting the following:

0^0 = Error [casio,sharp,etc]

or

0^0 = 1 [windows calculator]

nothing^0 = error

or

0^0 = error

<-- I believe this should be the right answer. Nothing divided by itself is theoretically either nothing and/or infinite. It is beyond conventional thinking.

The windows calc. gives a wrong answer in this case.

[Guitarist2098]

Less Is More, when i study with Sal's vids I feel its easier to learn with a short simple explaination compared to a long strung out explaination that gives me migranes and just flat out pisses me off for existing, Loving Sal's Vids

[asmenimi]

What a lovely, simple explanation.

[opokuansah]

is it 1over a or a over 1?

[amenohi3]

This is amazing. I wish I would have been taught mathematics this way in high school instead of as a set of ambiguous rules with no explanation of how those rules came to be. Thank you so much.

[Tejkmihowm]

it's sooo fazzinating! a^0=1. woow

[davidovich00]

dude that´s too fucking easy to xplain in 4 minutes.

[MegaShadowslayer]

@=D <<<<<<<<<, You Have the Noggin of Smartness

[AquaCatClaws]

my math book is sooooo nutheaded it doesnt explain anything like this infact it doesnt even hv this ...this ....a^9 or watevr u call it in it and i am doing prealgebra and this is new to meeeee.....thx sal...ur the real one teaching me math .... :-)

[mattttttheww]

u rule

[dudesinmaine]

Thanks- you saved my math homework!!

[Wafflesmart]

a=2

[thehollyjack]

thanks a lot i didnt get why a^0 was 0 and my dad told me a complicated definition but i get everything :)

[thehollyjack]

*a^0 was 1

[theboombody]

This is a very good argument, and probably is the main reason the convention of a^0=1 is trusted. But I still have my doubts. If you add 7 a total of 5 times, you get 7x5=5. If you add it a total of zero times, you get 7x0=0. So if you add a number to itself no times at all, you get nothing, which makes sense. However, if you multiply 7 by itself five times you get 7^5=16807. If you multiply 7 by itself zero times, you get 7^0=1. So if you multiply something by itself no times you get 1.

[theboombody]

Multiplying something by itself no times at all should give you nothing, just like if you add something to itself no times at all. I think my argument is pretty intuitive even though it isn't an accepted mathematical postulate.

[tackam]

This is great. I've been using this forever without understanding it.

[JeppeMajlund]

The definition is not general.. It's only defined for "a different from 0"..

If not, you would be dividing by 0, which is illegal (by the laws of - was it the inventor of math, you called him?)

[arklad]

Dj LARRY!

[mekaview]

you are amazing. thanks.

[vickiormindyb]

So it's arbitrary w/ a good reason?

That's the first time I've heard of Mathematics being something somebody decided, but I think it's awesome.

[teledynepost]

All mathematics is 'arbitrary' in a sense. People decide what symbols represent and what the rules are. Somebody came along and defined an exponent, it makes sense that you divide by the base as the exponent decreases, since to get to higher exponents you multiply by the base, you are just going back in the other direction and 'un-doing' the multiplications. You can also think of all exponents such as 2^3 as really being 1*2*2*2=8. 1 times anything does not change it ( 1*16=16, 1*700=700)

[theboombody]

You can invent new mathematics if you want. As long as it's consistent within itself, it counts. Of course it helps if it's consistent with the mathematics already established, but that's not necessary.

[choshacao]

If a^0 does not have a real value, what does this mean for a logarithm such as log(a)1=x, where the solution to x is said to be 0? It cannot be because a^0 has any real property of equaling 1?

[choshacao]

I think I confused myself. "a^0" and "log a 1 = 0" are the same thing written two different ways.

[calexculux]

Can you post logarithms questions an solving vidoes?Thanks!

[FaIseHope]

when i was in class i just learned that when you have a negative exponent you move it to the denominator and put one as the numerator or put it in the numerator if its in the denominator, it was a lot simpler for me

[slaid12345]

i stoped at 11 u nerd

[riversonthemoon]

Thank you. Great way to explain it.

[jdrizd2]

I understand that a is variable. When stating 7 to zero power is one, the only reason behind that is to carry the exponent into negative with fractions?

[jdrizd2]

Does the same intuitive definition hold true a negative value of a? -a zero power?

[winterstellar]

Mathematics is beautiful. 5 stars.

[LegoScout09]

@winterstellar math isnt beautiful, just khanacademy

[winterstellar]

@LegoScout09 I agree with you on khanacademy being beautiful. I have learned so much here, and if I were to keep just one subscription, it would be khanacademy. : )

[Nesti20993]

@winterstellar Mathematics are like womens, they are beautiful, but sometimes hard to understand HAHAHAH lol

[winterstellar]

@Nesti20993 : )

[bradq]

kewl

do you have any info on geometric tolerancing and true positioning. shop math. I work as a machined parts inspector and there is always controversy over what means what.

thanks for your vids. I think it is very kewl that you provide this info even though sometimes I have no idea what you are talking about. Indolent? Maybe just tired.

Thanks again.

bq