Understanding Exponents and Their Operations

[@starjumperrr]

i love how you show how the rules make sense instead of just saying "these are the rules" like my teachers did

[@Stoirelius]

They couldn't even explain it even if they wanted to.

[@ーーーーーー-g2b]

​@@StoireliusThus meaning they themselves didn't understand the subject good enough. Trying to explain something to someone else is actually a good test of your own knowledge.

[@Parmajyothi]

If your teachers are explained in this way you never gona check this LOL😂

[@Dreamprism]

@@ーーーーーー-g2bI say often to my own students that explaining to someone else is the best way to learn. So, if a student seems to have some grasp on the concept, I like to see if they can "teach me", and I will point out any flaws or gaps in the explanation. Yes, sadly there are many teachers who don't know why things are true and just insist some students do it a certain way. I remember in 7th grade my math teacher marked me wrong for something that I actually did correctly, because she misremembered something a past teacher had taught her and she didn't understand how it actually worked (or perhaps the past teacher just explained it wrong). I was also the go-to teacher at a summer program for other students to get help understanding some math concept if they weren't certain, and I was a little dismayed at one teacher not having a good idea of how phase shifts worked when she was supposed to be teaching a Precalculus/Trigonometry class. I taught her and she seemed to grasp it in the moment; I hope she retained it well enough to teach her class. One last bit of irony is that when I took a College Geometry class designed for math education majors in university, the math majors like myself generally performed significantly better in the class than the math education majors. Honestly, I guess it makes sense that people going purely into math would understand math better than those aiming to be middle and high school math teachers would, but it's still a bit sad that it means our young students don't get as strong a math education as they deserve.

[@alexlawson4173]

@@ーーーーーー-g2b my favorite teachers would have us students teach each other after theyve taught us. it helped the kids who didnt get it understand because their peers would teach in different words and it helped solidify knowledge and root out blind spots in the kids who were doing the second hand teaching.

[@Risk-on1]

I'm 30 and have gone through several maths, (though its been several years) and this is still one of the best explanations I've seen . Thanks prof. Dave!

[@_Kite_]

Am 18, and the use of calculator have mess my brain now am going over the basics to never user a calculator again.

[@inquinimaris]

Oh hey, good to see I'm not alone who decided to refresh on math (for whatever reason) at their 30s

[@plueychews1349]

​@@_Kite_lol it's true but you still need to use a calculator, just so you don't fumble on huge numbers

[@tramarthomas6105]

6:38 By cancel, him means that the X's divide by each other, and a number or term divide by itself is equal to 1. I dont know why i struggled with understanding that, but hopefully i helped someone

[@iburnvampiresforfun8095]

yes you did, thanks

[@fragglyone7607]

As complicated as this seems to me, it's very much better understood now that you explained it to me and I will practice this until I have it down just right. Thank you for your generosity, you are truly changing people's lives with your knowledge and I am very grateful for it!❤

[@jefflewis1338]

Gee thanks, at 75 years old I have relearnt exponents in a few minutes. Now I can attempt MindYourDecisions' probelms

[@ShifanawazWellnessPlaceForYou]

Way to go..!

[@yumeno-w-]

im 15 and woa :00 i kno dat channel!! i dont rlly understand anything tho t.t hopefully i get to ur level somedey,, i would love to binge math vids all day long because im so far behind in school but i dont have time now since i need to catch up on so many subjects that i dont even get time to understand or comprehend just mug up :c waaahhh i hate school,,,,,,, whenever i try studying i fall asleep so now im so so far behind T.t im trying my best to stay awake..

[@lazyylizzie]

@@yumeno-w- good luck!! i am also behind in school so i relearn basic math to catch up TT

[@Sai-e5b]

​@@yumeno-w-vent: I wanted to say horrible slurs after seeing this comment it filled me with such rage

[@aritte]

@@Sai-e5b real

[@teslauzair4539]

Prof. Dave is a wise man.

[@Muichiro-dc8up]

true

[@PalasBrown]

now I know why negative exponents are equal to 1 divided by base to the power, i love how you explain what, and why about the rules

[@ljr6490]

This is a revelation to me. I knew that negative exponents were inverse but now it actually makes sense as to why that is..

[@yuinurahilyon5711]

What an interesting legend 🤔 quintillion of rice which could cover the entire India by 1 meter, many families wouldn’t have a problem with food if that was the case. I never thought that I could enjoy Mathematics as much as I learn from you... I strangely feel joy from doing mathematics even if there was mistakes in my calculation. It seems like school doesn’t really offer too much joy in learning towards these amazing concepts. All of them are just full of serious calculations like it was depending on their honor and dignity like what the hell hahaha. Thanks for the lesson as always Professor Dave!

[@larrykent196]

Dave, nice job. I started with a interest in bacteria and watched those, good job. I did some digging and find you also have mathematics videos, quite complete too. Impressive. I like your brief yet direct to the point style. I will share these at every opportunity. Good job, I wish you the best and thank you.

[@christinasmith5373]

Thanks professor Dave! Doing my last GED test today. Didn’t pass math test in first try. You’re videos are helping me remember the things I’ve forgotten from math class at a much faster rate then I learned it originally

[@nezz0r]

What is 0^0? a) 1 b) Undefined Check Wolfram, your calculator, google calc and Operation system calc (for example windows) to take a look at the results.

[@aritte]

its undefined because if we could go by the rule that x^0 = 1 or 0^x = 1 we get 2 different results so its just undefined

[@nezz0r]

@@aritte What I meant is that we get different results by different calculators. If you use the google calc you actually get 1 same with windows calc. Try it out. Then try out wolfram alpha and you get undefined. -- Well if we would have 0^0 = 1 then there would be no problem for x^0 = 1 and 0^x = 1 if x = 0 though. And as far as I know if we can exclude negative numbers then 0^0 is actually 1. I think in combinatorics it is defined that way. There is also a reason why we can not approach 0^x from the negative side. Because if we do then we actually divide by 0. For example: 0^(-1) becomes 1/0. Actually any negative exponent creates that situation with 0. Here is an interesting idea though in regards to the positive side: The neutral element of multiplication is 1 and the neutral element of addition 0. So we can say: 0^3 = 1 * (0 * 0 * 0) = 0 0^2 = 1 * (0 * 0) = 0 0^1 = 1 * (0) = 0 0^0 = 1 Because now we have an absence of 0 to multiply and only the neutral element is left. This would also work with other numbers: 2^3 = 1 * (2 * 2 * 2) = 8 2^2 = 1 * (2 * 2) = 4 2^1 = 1 * (2) = 2 2^0 = 1 What do you think?

[@davidzubiria3783]

I enjoy the infinite bliss and enjoyment your face expresses in every lesson. Thank you...

[@Stoirelius]

You're not very good in reading facial expressions, then. That, or you're imagining things. He clearly has a "bored to death" look in all of his videos. What do you see in his face to make you say such thing?

[@davidzubiria3783]

@@Stoirelius irony

[@LC-yv9ey]

Great videos, thank you for helping me understand math, I can't wait till I can do linear algebra 😂

[@Blue__Strawberries]

Same😊

[@Stoirelius]

Have you got there yet?

[@sakshamgoel1957]

Great going sir

[@rinyeongi6322]

Thank you so much mr. Dave this helps me in many ways possible

[@jayw8726]

With this video, you entered Middle school Math from Primary school Math. 😁👏

[@ini_titi]

and here's me from vocational high school 😂

[@theclassyphilosopher]

Thank you man , god bless you

[@Jasmita-8]

Thx for the beautiful session professor Dave!

[@mysterioussoup3393]

I'm confused. Did he ever explain what inverses were? I'm stuck on negative exponents 4:47.

[@mysterioussoup3393]

Nvm I get it now lol

[@vathsalaa2774]

That story was quite interesting 😃

[@BlockStah]

Congrats, you have 10 squared likes

[@kartikiyer3067]

It is moving towards 7³ likes

[@Digitalbandits99]

Now it is 11³ likes... And 5² dislikes...

[@Pedroharada]

@@Digitalbandits99bro replying after 2 years 💀

[@Digitalbandits99]

@@Pedroharada what do you mean?

[@futjr6969]

professor dave on top

[@alyxkrieger6764]

i just so happen to have trouble with 7's and 9's. thx for the mental exercise!

[@Signalislost]

Professor dave explains ❤❤

[@demetriushiscox7045]

Dude half of this video is things my school refuses to cover... I'm in high school

[@ravitejasusarla9488]

More useful

[@IrinaBautista.]

I always knew that home/self study will work to me no communication barrier

[@Garfield_Minecraft]

^4 tesseracting the number?

[@InverseBasement]

I got this far and math is starting to make sense o.O

[@BenMordecai]

Is 0^0=1? If so, why?

[@GRosa]

In Algebra, 0^0 is not defined. For Calculus, you may want to see this video: kzbin.info/www/bejne/sKq0pYFtj8ecY8U and/or this one: kzbin.info/www/bejne/pZSTfmSlbdmohtE

[@BenMordecai]

@@GRosa that was a great video. Bringing back some really rusty math memories from college.

[@GRosa]

@@BenMordecai You're welcome, I'm glad you enjoyed them. Shalom

[@luamfernandez6031]

Because: X^2 × X^0 = X^(2+0) = X^2 then the value of X^0 must be be one because for any multiplication to result in the same as one of the factors, some factor must be one. X^2 × X^0 = X^2 × 1 Could I get my point across?

[@Dreamprism]

On a technical level, the reason we define negative and zero exponents the way we do is so that the exponent rules (that we can already prove work for positive integer exponents) will also work for zero and negative exponents. So, we are not using the rules toward the end of this video to prove what negative exponents already mean; we are proving what we must define negative exponents to mean in order for our exponent rules to remain consistent. It's a subtle distinction but useful for people to understand as they get much deeper into math. It can also be applied to situations like the gamma function being consistent with [a translation of] the factorial function. Is "(-1/2)!" actually equal to "Gamma(1/2)" and therefore "sqrt(pi)"? Not really... or at least it's questionable.

[@user-sq8hq9mh9o]

‏‪6:41‬‏

[@thedisintegrador]

great

[@JohnPaul-v2f]

0:03

[@Deen837]

Im on 4th class and im smart because of you!

[@dariusanderson2417]

I love the intro

[@derrickmcleod]

Who was the one doofus, who didn't like this video.

[@MrFrogmanYT]

I know this was 4 years ago so you might not respond but why can't you add together numbers with different variables?

[@caronfernandes4625]

Because the two different variables represent two different things that do not mix.

[@JoelMcCary]

7c3 is 343 9c4 is 6561 (xc4)(xc6) is x2 (xc9)/(xc7) is x10 and (c5x)c3 Is x15

[@agentstona]

You explained in 10 minutes what my dumb asss primary school , high school and university teachers could not explain to me over 14 years of my studies .........i wish i had found your videos earlier.

[@samkurtz1942]

It would be cool if you could explain proofs(geometry)

[@ProfessorDaveExplains]

just gotta get through some algebra and then i'll be on geometry!

[@preparationoftheelect2023]

Man that was difficult 😅 But ill get there by Gods grace

[@ljr6490]

Good luck!

[@Sec0ndSqu4re]

I like how he shows summation Σ

[@Sai-e5b]

🗿🗿 sigma

[@rishik2734]

The person who disliked was the king

[@clipchampion7594]

lol hi this is tanish im reviewing for final hi rishi

[@rishik2734]

@@clipchampion7594 hi tanish

[@2gen_alharic]

Bro is staring into my soul When you do a PowerPoint presentation but you are socially awkward

[@Sai-e5b]

Diddy party thanks bro🎉

[@KevenPena-br6nj]

5² + ( 5 × 2 ) - 4

[@windowsmercurySP13]

That's 31

[@awaistechnology9048]

31 is answer\

[@stephend.4342]

It’s the summation (sigma) where n starts at zero (so that the first square has one grain of rice) and the last (64th square) has 2 to the 63rd power grains of rice, the summation of this sequence of 64 numbers then being about 1.8 times 10 to the 19th power, which is 18 quintillion grains of rice.

[@robloxflopsyyt7068]

This is amazing but I gotta point out.... YOU SAID ONE FOURTH?

[@saladedefruit2529]

I thought the king murdered the wise man when he realised the number.

[@GirlSchool-hg7pw]

I skipped some video but i really need to

[@TherealYUVRAJ]

Old Indian Legend

[@mamadwali4278]

❤❤❤❤

[@SquatyDog]

I would like one quintillion rice grains please

[@nazarderevyanko8980]

Double it and give it to the next person

[@shanmukhmanepalli]

i am from india

[@davidzubiria3783]

x/\0 doesn´t make any sense to me.

[@comunoko]

X gon' give it to ya (what)

[@Mannat1001]

Anyone from india in 2024

[@LUV_YIN]

WHY

[@JohnPaul-v2f]

uh

[@forstudypurpose8380]

Of course disliker are Teacher XD lol

[@ahmadtannir8742]

This is cracked

[@chourouk-gr9qg]

:D

[@damnnn.]

i like your videos but i hate the intro