Harvard University Simplification Tricks || Power Rule Aptitude Test || Calculators NOT allowed

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Super Academy

Күн бұрын

Пікірлер: 350

@mr.parabola7447 26 күн бұрын

You are the best example of how an easy thing can be made tough 👍🏻👍🏻

@superacademy247 26 күн бұрын

I aim to make you think deeper! 😎💯Thanks for sharing your perspective! 🙏

@MrThorAss Күн бұрын

@@superacademy247 In a couple of steps 2^(-3/8)

@boeubanks7507 Ай бұрын

Good god. This is why people hate mathematicians. You literally made the problem ten times harder than it has to be. I am a trained physicist, and I found this excruciating. I can just imagine the middle and high school students watching this.

@superacademy247 Ай бұрын

I’m glad you found a more efficient method! 🔥 💯. It’s all about finding the most suitable representation! 😎 Thanks for your feedback! I appreciate your perspective! 💖💯

@KyosukeNanbu-s7c Ай бұрын

@@superacademy247 I think he was saying you have expounded too much when it has simple solution... 1/(2)^3/8 but seriously, 1 over 8th root of 8 is what it is...

@ХаткиЧиль Ай бұрын

Я тоже устал смотреть как разжовывают одни и те же правила, и по два раза переписывают одно и тоже 🤦‍♂️ Такое ощущение что аФтАр преподает для дебилов имеющих память как у рыбки гуппи 🤦‍♂️

@TheDavidlloydjones 27 күн бұрын

@@KyosukeNanbu-s7c ちょっと違う!! It's 1 over the cube root of one eighth. Today you went South a little bit: 今日は少し南部 🙃

@BrunoBezerra058 17 күн бұрын

@@superacademy247 GOSH, you're a angel! ❤

@假老二 3 ай бұрын

2^(-3/8) is more directly

@TheDavidlloydjones 27 күн бұрын

Well done.

@అధునాతన_సనాతని 16 күн бұрын

😂😂

@brunodiazdiaz Күн бұрын

I did it in my mind.

@rameshgudadhe9346 3 ай бұрын

Problem can be solved in two steps

@TheDavidlloydjones 27 күн бұрын

It can be solved in one. It's 0.71 by inspection.

@emmanuelfreeman708 2 ай бұрын

This is one of the teachers or instructors that made students afraid of mathematics. See how he took over 10 minutes to solve a problem that can be solved in less than 1 minute. Students will now think that it is a huge headache to solve such a problem.

@CriticSimon Ай бұрын

That's not the idea. If you solve a problem in 1 minute, nobody will watch it. If the video is at least 8 minutes long then it brings in more revenue because of the ads and that's what YT is going after, of course. More profit to the detriment of YT'ers!

@sudhakaranpillai9623 3 ай бұрын

The most stupid way of solving a simple problem.You are testing the patience of the viewers.

@superacademy247 3 ай бұрын

Don't worry, you're under professional control.

@DrBenway97 3 ай бұрын

@@superacademy247 What is that supposed to mean?

@ivanballeram6112 3 ай бұрын

This is only one of the solution.Actually there are seven more roots.So this problem has eight roots,two are real and other six are comlex.This according to fundametal theorem of algebra.

@CriticSimon Ай бұрын

unfortunately, YT pushes these videos to a lot of viewers and it gets lots of views. There's something stupid about the algorithm, not the video. The video is pretty basic but either, that's what people click on or YT recommends these kinds of videos to more people than videos that are a little bit more challenging. They definitely changed something to reward these kinds of videos. I agree, it's click-baity. I don't think this problem came up on a test at Harvard. Sad but this is the reality.

@venugopalramachandran6766 3 ай бұрын

1/8 is 2^ minus 3. So LHS is 2^ minus 3/8. which is 2^5/8 /2 on multiplying by 2/2.

@hafeezrehman8692 2 ай бұрын

Answer is more complicated than Question ❓

@TheDavidlloydjones 27 күн бұрын

Most of these fancy questions have answers that are just as simple as the questions. The people who can see the simple answers go to Harvard. The people who dream up complicated routines get to be tax collectors in Hyderabad They then steal either three or five eighths off the top before forwarding the rest up the line to New Delhi.

@sujoydas9273 3 ай бұрын

This is not tricks, but it is a long journey trip.

@superacademy247 3 ай бұрын

It's rationalizing the denominator

@roshlew6994 3 ай бұрын

Yes . Stupid long vedio for nothing

@prajaktab7010 3 ай бұрын

This could be solved with in only five steps.

@nagarajahshiremagalore226 3 ай бұрын

Yes, I agree

@nagarajahshiremagalore226 3 ай бұрын

Damaging the Reputation of Harvard University.

@virgilios.perdigonjr.6840 2 ай бұрын

The final form is more complex than the given!

@ManjulaMathew-wb3zn 2 ай бұрын

The easier approach is to multiply the denominator and numerator of the expression inside the bracket by 2^5. Then the expression becomes (32/2^8)^(1/8) thus the answer. I have seen another video of yours regarding (1/9)^(1/9). The answer for that would be (3^(7/9))/3 The fact of the matter is that the answer is not any simpler than the question. If the question had 1/5 the answer would be (fifth root of 625)/5. Can do it almost by memory.

@Mountainlion-d5h3c 3 ай бұрын

Extremely boring. Writing the same thing over and over every line . It should take more than 30 secobds.

@sundaramsadagopan7795 3 ай бұрын

Taking more time even for simple thing to earn, I think.

@CriticSimon Ай бұрын

@ninadomshoeva8725 23 күн бұрын

Возмущалась, но досмотрела😂

@MataniMath Ай бұрын

One of the characteristis of mathematics is that it makes difficult things easy. This actually complicates what is easy

@TheDavidlloydjones 27 күн бұрын

Which is why a.) it gets the wrong answer, and b.) shows the guy has missed the whole essence of *all* these Harvard entry japes.

@poseidon8189 18 күн бұрын

Totally agreed !

@walterwen2975 3 ай бұрын

Harvard University Simplification Tricks: (1/8)¹⸍⁸ =? (1/8)¹⸍⁸ = (1/2)³⸍⁸ = (1/2³⸍⁸)[(2⁵⸍⁸)/(2⁵⸍⁸)] = (2⁵⸍⁸)/[(2³⸍⁸)(2⁵⸍⁸)] = (2⁵⸍⁸)/(2⁸⸍⁸) = (⁸√32)/2

@henripangaribuan2182 3 ай бұрын

Very simple

@namsawam 2 ай бұрын

(⁸√32)/2 = 1/⁸√8 is most simple and super trivial.

@kas138 Ай бұрын

Stupid Harvard that you long solution man but this short

@TheDavidlloydjones 27 күн бұрын

Well done. And elegantly typed! And "Wen" is medieval English for "to know." 😂 Come to think of it, a Walther is a hand gun, very effective at point-blank range.

@rangarajanvenkatraman762 3 ай бұрын

Lot of repeated steps.

@superacademy247 3 ай бұрын

To make everyone find it easier to understand

@narolenkoaleksandr58 3 ай бұрын

Открыл сумочку, достал кошелёк, закрыл сумочку,открыл кошелёк, достал билет, закрыл кошелёк, открыл сумочку, положил кошелёк....

@IRVINMILLER Ай бұрын

(1/8)^1/8= 1/(((8^1/2)1/2)1/2) =1/((2*(2^1/2)1/2)1/2)=(2.828)^1/2)1/2 the rest can be done using the manual technique for finding the square root. You faied your own test.

@superacademy247 Ай бұрын

I appreciate your method, it's a creative approach to simplify the expression. 🙏Thanks for pointing out the mistake, I'll make sure to review my calculations carefully. 😅💯

@Himasthla 2 ай бұрын

Too long! { 1/a=a^-1 } (1/8)^(1/8)=(2^-3)^(1/8) { (a^b)^c=a^(bc) } (2^-3)^(1/8)=2^(-3/8) rationalization: { 1-1=0 } { a^(b+c)=a^b*a^c } 2^(-3/8)=2^(1-3/8-1)=2^(5/8)/2 or 32^(1/8)/2

@rakeshsrivastava1122 3 ай бұрын

The simplification has yielded a complicated answer.

@superacademy247 3 ай бұрын

Not complicated because the denominator is finally rational

@TheNizzer 3 ай бұрын

Trivial. 1/8 = 2^-3. 2^-3^1/8 = 2^-3/8. Hardly difficult.

@whoh3222 Ай бұрын

Take log base 2 first, then the equation transforms -3/8

@rainbowgood-df6vc 3 ай бұрын

why to do all that ???

@superacademy247 3 ай бұрын

To rationalize the denominator completely

@DrBenway97 3 ай бұрын

@@superacademy247 Completely..? Can it be rationalized partially..? LOL Come on man, do better...

@daniellerosalie2155 3 күн бұрын

Can't we take (1/8) as 2 to the negative 3 to the (1/8)? Then we multiply the exponents -3(1/8) to get 2^(-3/8)? I saw how you started the problem, and it does work that way, but it is long.

@superacademy247 2 күн бұрын

Thanks for sharing your perspective but a negative exponent in the numerator is like a radical denominator. Go a step further to make the exponent on the numerator positive.✅🚀💖💯👍🥰🤩😎

@milanpilny5008 3 ай бұрын

Know anybody longer way to solution?

@pvinvs 3 ай бұрын

Is he amateur of Math? lhs=(2^(-3))^(1/8)=2^(-3/8). His way is not elegant.

@mattiasneuman7593 3 ай бұрын

2^-(3/8) in 2 steps

@ikennaodii6746 3 ай бұрын

Sorry, you practically did nothing but time wasting

@superacademy247 3 ай бұрын

I rationalized the denominator successfully and completely

@schneider.mariane 3 ай бұрын

@@superacademy247And why not simply 8 ^ (-1/8)

@chadwagoner7056 14 күн бұрын

I personally need this kind of help. I have a hard time not thinking about every step to make sure I understand every single aspect of the problem rather than solving it with a memorized set of rules. I still don't understand this, but I understood the rule set. I will have to look further into why some of the rules are what they are, though. It sucks to have to do it this way, but I cannot make myself turn off and turn out.

@superacademy247 13 күн бұрын

Thanks for sharing your perspective on problem-solving. It's great that you're determined to understand the underlying principles! 💯💕💪I hear you! It's definitely challenging to balance speed and understanding. Keep up the hard work! 💪💕🤩

@chadwagoner7056 13 күн бұрын

@superacademy247 Oh, far out! I didn't think anyone at the site would pay attention to this comment. I watch your stuff everyday now. I decided a few months ago I was going to polish up my math skills before I started looking for partnering with a university in Europe for a PhD program. I realized very quickly that the memorized rules as an undergraduate were no longer with me. The reason I don't remember them is the reason I try to gain the concepts that create the rules. This also added a year onto my graduation time so those years ago so I stopped thinking, got a tutor, went twice a week, and memorized enough to get through calculous. For me, Algebra was much harder at the introduction stages. Once I knew the reasons to the rules I could speak the language. For the life of me I can't believe I did it now. It was the difference between one Bachelor or two so I figured, "why not?" Regardless, I like your presentations. I ignore the "subscribe" segment, because I already subscribed. I understand you need people to recognize your work so that you can continue to do this. If I can't get caught up, at least to pre-calc, by Spring I'll probably take your full course. My old nemesis time continues to creep up on me though. Thank you for your work! Chadillac

@superacademy247 8 сағат бұрын

Thanks you very much for your kind words. I'm humbled.🙏🙏🙏

@URMBOT 3 ай бұрын

Much tooooo long...! 😴

@BN-hy1nd Ай бұрын

Since 8 is the same as 2^3, why didn't you do (2)^(-3x(1/8)) ie (2)^(-3/8) ? Which is the same as your answer simplified because 32 = 2^(5/8) and 5/8 - 1 = -3/8 because 1/2 is the same as 2^(-1)

@hermantopurwadi5247 2 ай бұрын

Why should rewrite the result of the previous equation again and again 😂

@superacademy247 2 ай бұрын

To emphasize

@СергейВикторович-ф5г Күн бұрын

Почему бы просто не возвести в степень числитель и знаменатель? И получить единицу деленную на корень 8 степени из восьми, или 2 в степени -3/8.

@goutamsarkar1686 2 ай бұрын

What a foolish approach.

@evetsnameloc6302 3 ай бұрын

Excruciating.

@superacademy247 3 ай бұрын

Energy usurping. Brute force!

@SafdarDurrani 22 күн бұрын

That was a simple question but you did not simplefy but extended and extended,, Thanx

@superacademy247 22 күн бұрын

Thanks for your feedback! 💯🙏It's a Harvard admission problem, so it's meant to be challenging! 💪💪💪

@CracksMeUp-182 3 ай бұрын

Sorry. It is not simplicity.

@rob876 Ай бұрын

1/8^(1/8) = 1/2^(3/8) = 2^(-3/8)

@superacademy247 Ай бұрын

Rationalize the denominator

@blacktamizans7847 Ай бұрын

You have complicated a very simple sum.

@superacademy247 Ай бұрын

I appreciate your feedback! It's all about finding the most efficient approach for these types of problems.Thanks for your input! I strive to provide multiple perspectives and techniques to help with problem-solving.💯💕🙏

@AndrewHwang-m1c Ай бұрын

1/8=2^(-3) and substitute into eq. => 2^(-3/8) = [2^(3/8)]^(-1) = [8^(1/8)]^(-1) = 1/[8^(1/8)]

@steveodonnell3030 3 ай бұрын

(2^-3) ^ (2^-3) = 2 ^ (-3/8) Done

@NickNoblePhotography 2 ай бұрын

Question is simpler than answer! You made it different and more complicated!

@kanguru_ 2 ай бұрын

Let a=(1/8)^(1/8), so a^8=1/8=2^-3, so a=2^(-3/8)

@IncoSoft2 2 ай бұрын

Sixteen minutes for this ? You call this a trick! Where is the trick? I think you have also a trick for 1+1 = ? like 1+1 = 1^3+1^4+0^4 because 1^a = 1 and 0^b =0 so etc etc... and your trick can last 18.8 millards years. I'm joking but I stopped the video before I bigbang.

@joeaberman449 3 ай бұрын

your method has some value in teaching laws of exponents and radicals .the answer could be (8)^-1/8 but i liked it it is .771105

@superacademy247 3 ай бұрын

Thanks 😊🤩🤩🤩

@biswanathbera1260 3 ай бұрын

Is it simplification or complexification?May I ask.

@superacademy247 3 ай бұрын

Rationalization

@biswanathbera1260 3 ай бұрын

@@superacademy247A long journey to reach just 1/ 8th root of 8.Anybody can reach there by two steps. Again a long tedious journey to reach the final answer . Answer is also not in simpler form. Please cut short the journey.

@todd8155 2 ай бұрын

It is a good review of the rules of exponents. Not an easy way to solve, but a good review none the less! Now if the instructions were solve this using all the known rules of exponents, then this is the way!

@ramverma9471 2 ай бұрын

😂नौ दिन चला अढाई कोस ।

@ashe792 2 ай бұрын

I just waste 16.5 mins watching all of this while an average Asian kid can solve this problem in 15 secs

@digbycrankshaft7572 2 ай бұрын

Appallingly longwinded and why leave it as (2^(5/8))/2 which is not simplified when you can reduce it to 2^(-3/8)?

@superacademy247 2 ай бұрын

The objective is to rationalize the denominator

@Budgeman83030 29 күн бұрын

So when he did the m - k and the n - k with k = 2. Was that due to the base number being 2?

@anabubalo3813 3 ай бұрын

Это как раз тот случай когда из мухи делают слона...

@superacademy247 3 ай бұрын

It's a special case in which an elephant is relegated to rodent class

@TapasKumarDe-jz4lz 3 ай бұрын

Foolish and unnecessary repeatation of the same steps

@Patrik6920 Ай бұрын

was this the lesson of how to make simple tasks complicated? .. must have missed that class in school its 2^-3/8 OR 1/2^3/8

@aqwseijnhy 2 ай бұрын

(a^n)^(1/n) is not equal to a exemple with n=2 and a=-5 sqrt(-5²)= 5 not -5 (a^n)^(1/n) = |a|

@НадеждаПавлова-ю3з 3 ай бұрын

Почему вы так долго решаете?Устно 2^-³/⁸,не хотите так,преобразуйте,как хотите,но не так долго.

@superacademy247 3 ай бұрын

It's long because it's a crash course for newbies

@actualRocketScientist 24 күн бұрын

That took way too long then you can do this in two steps first eight is 2 to the 3rd power and then you apply the 8th route to both on top of the bottom and just multiply the exponents which would be 2 to the third power times one over two thirds

@sundaramsadagopan7795 Ай бұрын

For repeating the same n times, the comment is "it gives rise to" .Unnecessary repetitions.

@АлександрКлевцов-ш4у 2 ай бұрын

Просто шуллер! Все мозги разбил на части,все извилины заплел!😂

@mykhaylodorozhovets6120 3 ай бұрын

янадзвичайно довге поясненя з багаторазовим повторенням того самого.

@THyperon 3 ай бұрын

It's after midnight... I couldn't sleep... I watched this over and over repeating of numbers.... chrrrr chrrrr zzzzzz.....

@DrBenway97 3 ай бұрын

An unnecessarily confusing and convoluted way of Rationalizing The Denominator...! Why not just explain it in a more straight forward way - which I'm pretty sure you know how to do. Sorry dude but this is the kind of thing that makes the average person think that math is really hard (which most of it is! but not this...)

@superacademy247 3 ай бұрын

KZbin gives us freedom to express authority over the topic 🥰. Can't you see the fascinating style I've deployed to rationalize the denominator in an elegant way?

@DrBenway97 3 ай бұрын

@@superacademy247 I'm sorry but confusing and unnecessarily complicated is NOT fascinating or elegant.

@LarbiZerguine 27 күн бұрын

Good thank you ❤❤❤❤❤❤

@superacademy247 27 күн бұрын

You are most welcome! Glad you enjoyed the video! 😁💯💕😎🙏

@l.w.paradis2108 2 ай бұрын

In problems like this, I would give the fast answer, then the long one. The irony is (and I address the critics) that PROOFS are often much longer.

@sankaranmurthy573 2 ай бұрын

(1/8)^(1/8) = a --> a^8 = 1/8 --> a = 1/eighth root of 8. I don't think much simplification is possible.

@albertnawab9211 3 ай бұрын

Waste of time. Waste of phone battery. Nobody use in daily life.

@superacademy247 3 ай бұрын

😂You make me feel like laugh. You're hilarious 😆

@carlossummers4992 3 ай бұрын

To evaluate the expression 1/8^1/8, we need to follow the order of operations (PEMDAS): 1. Exponentiate 8 to the power of 1/8: 8^1/8 = 8^(1/8) 2. Take the reciprocal of the result: 1 / 8^(1/8) Using a calculator or solving algebraically: 8^(1/8) ≈ 1.297379 1 / 1.297379 ≈ 0.77037 So, 1/8^1/8 ≈ 0.77037.

@RyanLewis-Johnson-wq6xs 3 ай бұрын

(1/8)^(1/8)=0.5Surd[32,8]=(Surd[32,8])/2 final answer

@boeubanks7507 Ай бұрын

You could solve this much easier and faster using exponents as verses roots.

@superacademy247 Ай бұрын

I appreciate the suggestion! There are often multiple ways to approach a problem! 😎

@Nikolaos.I.P 17 күн бұрын

too much trouble for such a minor problem 8^(1/8) = 1/(8^(1/8)) and 1/(8^(1/8)) = 1/2^(3/8) and 1/2^(3/8) = 2^(-3/8)

@adgf1x 3 ай бұрын

x^8=2^-3=>x=2^-3/8.ans

@TheDavidlloydjones 27 күн бұрын

This is all incorrect. The eighth root of anything is the square root of the square root of the square root. Here that comes down to 1/(2^.5) or half of the root of two, i.e. roughly 0.71.

@is7728 3 ай бұрын

(1/8) ^ (1/8) = ^8√ (1/8) = ^(2*2*2) √(1/8) = √√√(1 / 8) = 1 / (√√√8) = 1 / ( 2^(1/4) * 2^(1/8) ) = 1 / ( 2^(3/8)) = 2^(-3/8)

@sharufun209 Ай бұрын

r u really from harvard university......i don't belive.....

@virgilios.perdigonjr.6840 2 ай бұрын

There are so many repetitions in the steps! Harvard applicants are supposed to be more intelligent than the host likes to project!

@keinKlarname 12 күн бұрын

Why not always = ?

@rainerzufall42 8 күн бұрын

A lot of unnecessary calculation... (1/8)^(1/8) = ½^(3/8) = 2^(-3/8) = ½ 2^(5/8) = ½ 32^(1/8).

@richardchiu9975 2 ай бұрын

wow, it takes hours to work one simple question ,too detailed steps makes it boring.

@aprotutor 3 ай бұрын

=(2^-3)^(1/8)=2^(-3/8)

@anatolijpachomenko8280 3 ай бұрын

Совершенно бездарное решение. При том, что задача решается устно.

@ლიასუთიძე 3 ай бұрын

ნერვებზე მომშლელია ასე დაწვრილებით წერა, პირველკლასელი ხომ არ უყურებს ?

@geosookim1838 Ай бұрын

I really do not understand, what this guy is doing. He is making a simple problem harder. What's the different between (1/8)^(1/8) and 2^(2/8) / 2?

@superacademy247 Ай бұрын

Rationalizing the denominator completely 🥰💯💕✅🙏

@ИванКудряшов-ы6э 2 ай бұрын

Конец решения и ответ некрасивые. Начиная с 11.45 все решается просто вычитанием показателей степеней и получается сразу нормальный ответ. И у меня в университете ваше решение с таким ответом посчитали бы незаконченым.

@superacademy247 2 ай бұрын

Incomplete how??? The criteria is to rationalize the denominator and I've done it. What else is required?

@DavisRimu 27 күн бұрын

You've earned the two marks for that question, now have you got time for the rest of the exam?

@iran-sweden 2 ай бұрын

You just make it complicated, (1/8)^(1/8)=1/(8^(1/8)=1/(2^(3)^(1/8))=1/2^(3/8) or 2^(-3/8) that's it

@harsharnjeetsingh9217 3 ай бұрын

Friend such problems can be solved with the help of logarithms if not using calculators.

@naveenpokala6442 Ай бұрын

Wrost method, poor understanding of this guy....he has complicated everything, lucky we can ignore him

@superacademy247 Ай бұрын

I've rationalized the denominator completely

@abdu5031 18 күн бұрын

complicate meth od

@ТамараМузыка-ж5е 3 ай бұрын

Зачем двадцать раз переписывать одно и то же?

@superacademy247 3 ай бұрын

To emphasize

@l.w.paradis2108 2 ай бұрын

Why not 2^(--3/8)?

@Армен-с4н Ай бұрын

Чем больше я слушаю такие каналы, тем хуже становится мое произношение... 😢

@superacademy247 Ай бұрын

And the better you become at Math skills 😍💕🤩

@rameshchander2702 Ай бұрын

Too much long procedure. Nothing told by you

@johnnyragadoo2414 3 ай бұрын

I solved this in my head before watching. It's easy when you see the tricks (I'm a math dummy, tricks are all I have). One to any power is 1, so the problem is to simplify 1/8^(1/8). Multiply numerator and denominator by 8^7/8 to get 8^(7/8) / 8. Subtract the exponents to get the answer, 8^(-1/8). Note that 2^(5/8)/2 is the same as 2^(-3/8), which is the same as 8^(-1/8). Nice scenic tour through lots of properties, though. I kind of like this sort of overcomplication. That bit about subtracting k is a little overcomplicated in itself. Subtracting a constant from like-base numerator and denominator is just dividing each by base^k.

@superacademy247 3 ай бұрын

The answer I obtained has more rational denominator than yours in my opinion which is the primary objective of my step by step process. Your answer and mine are the same but the form matters.

@johnnyragadoo2414 3 ай бұрын

@@superacademy247 The denominators in my answer, 8^(-1/8), are one in the base, 8 in the exponent. Your answers were pretty much the same, aren't they? Just trying to learn, and I appreciate your channel. I often find simpler methods, but that makes for a nice learning experience.

@TWJRPGGamming 2 ай бұрын

2^(-3/8)

@明世塵 2 ай бұрын

講解十分清晰

@superacademy247 2 ай бұрын

Thanks 👏👏👏

@clivetooth 13 күн бұрын

Totally ridiculous. As others have noted the question is trivially easy, and the final answers are not particularly simpler than what we started with.