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

[@mr.parabola7447]

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

[@superacademy247]

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

[@MrThorAss]

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

[@cradleofrelaxation6473]

😂 😢😅

[@Mathguy1729]

@@superacademy247 It seems that you don’t quite understand his sarcastic tone.

[@boeubanks7507]

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]

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]

@@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]

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]

@@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]

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

[@emmanuelfreeman708]

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]

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]

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

[@superacademy247]

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

[@DrBenway97]

@@superacademy247 What is that supposed to mean?

[@ivanballeram6112]

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]

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.

[@BN-hy1nd]

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)

[@rameshgudadhe9346]

Problem can be solved in two steps

[@TheDavidlloydjones]

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

[@TheDemoniodelaSelva]

No simplificó, cuando debía de hacerlo.

[@MataniMath]

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

[@TheDavidlloydjones]

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]

Totally agreed !

[@假老二]

2^(-3/8) is more directly

[@TheDavidlloydjones]

Well done.

[@అధునాతన_సనాతని]

😂😂

[@brunodiazdiaz]

I did it in my mind.

[@baselinesweb]

@@brunodiazdiaz Aren't you special!

[@virgilios.perdigonjr.6840]

The final form is more complex than the given!

[@venugopalramachandran6766]

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

[@sujoydas9273]

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

[@superacademy247]

It's rationalizing the denominator

[@roshlew6994]

Yes . Stupid long vedio for nothing

[@prajaktab7010]

This could be solved with in only five steps.

[@nagarajahshiremagalore226]

Yes, I agree

[@nagarajahshiremagalore226]

Damaging the Reputation of Harvard University.

[@Mountainlion-d5h3c]

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

[@sundaramsadagopan7795]

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

[@CriticSimon]

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.

[@ninadomshoeva8725]

Возмущалась, но досмотрела😂

[@hafeezrehman8692]

Answer is more complicated than Question ❓

[@TheDavidlloydjones]

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.

[@narolenkoaleksandr58]

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

[@danielberttolini6292]

Jajajajaja

[@ManjulaMathew-wb3zn]

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.

[@rakeshsrivastava1122]

The simplification has yielded a complicated answer.

[@superacademy247]

Not complicated because the denominator is finally rational

[@walterwen2975]

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]

Very simple

[@namsawam]

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

[@kas138]

Stupid Harvard that you long solution man but this short

[@TheDavidlloydjones]

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.

[@TheNizzer]

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

[@rangarajanvenkatraman762]

Lot of repeated steps.

[@superacademy247]

To make everyone find it easier to understand

[@Himasthla]

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

[@cradleofrelaxation6473]

You’re a legend!! All the laws of exponents have been used successfully!!

[@superacademy247]

Thanks for your kind words.🎁🎉🥳🎄🌲

[@mattiasneuman7593]

2^-(3/8) in 2 steps

[@ashe792]

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

[@whoh3222]

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

[@IRVINMILLER]

(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]

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. 😅💯

[@steveodonnell3030]

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

[@daniellerosalie2155]

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]

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.✅🚀💖💯👍🥰🤩😎

[@pvinvs]

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

[@URMBOT]

Much tooooo long...! 😴

[@evetsnameloc6302]

Excruciating.

[@superacademy247]

Energy usurping. Brute force!

[@NickNoblePhotography]

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

[@hermantopurwadi5247]

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

[@superacademy247]

To emphasize

[@SafdarDurrani]

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

[@superacademy247]

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

[@ikennaodii6746]

Sorry, you practically did nothing but time wasting

[@superacademy247]

I rationalized the denominator successfully and completely

[@schneider.mariane]

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

[@TapasKumarDe-jz4lz]

Foolish and unnecessary repeatation of the same steps

[@milanpilny5008]

Know anybody longer way to solution?

[@Mathguy1729]

Use the definition of non-integer exponentiation, i.e. eˣ = Σₙ xⁿ/n! , together with the definition of natural logarithm, i.e. ln(x) = ∫₁ˣ 1/t dt.

[@chadwagoner7056]

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]

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]

@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]

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

[@kanguru_]

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

[@goutamsarkar1686]

What a foolish approach.

[@Just-rm]

The simplest answer is 1 over 8 root 8th.

[@superacademy247]

Watch the video and see how we got the answer! 🤯

[@l.w.paradis2108]

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.

[@anabubalo3813]

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

[@superacademy247]

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

[@AndrewHwang-m1c]

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

[@rob876]

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

[@superacademy247]

Rationalize the denominator

[@rainbowgood-df6vc]

why to do all that ???

[@superacademy247]

To rationalize the denominator completely

[@DrBenway97]

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

[@EddyHuiLapWaiSaysGoodLuckToAll]

not simplify , you are rationalizing it , simplify it that means 2^(-3/8)

[@superacademy247]

I appreciate your feedback! I'm trying to show ways to rationalize expressions without calculators.

[@СергейВикторович-ф5г]

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.

[@X00000370]

Some good Algebra Radical/Power demonstrated but student attention span would have been challenged...

[@blacktamizans7847]

You have complicated a very simple sum.

[@superacademy247]

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.💯💕🙏

[@IncoSoft2]

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.

[@stevenwitts6968]

😂😂😂he could have spent two hours working out 1+1

[@biswanathbera1260]

Is it simplification or complexification?May I ask.

[@superacademy247]

Rationalization

[@biswanathbera1260]

​@@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]

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]

😂नौ दिन चला अढाई कोस ।

[@aprotutor]

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

[@joeaberman449]

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]

Thanks 😊🤩🤩🤩

[@boeubanks7507]

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

[@superacademy247]

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

[@BartBuzz]

Why is the new expression considered to be "simplified"? The original expression can easily be computed using a calculator. The 16+ minutes you spent simplifying was a waste of time. (1/8)^(1/8) can be written as 2^(-3/8) by inspection.

[@jean-yvesbeguec9944]

Have you ever considered changing career ?

[@Roq-stone]

The 8th root of +1 can be */-1. But because you are using surds I will forgive you. This is like walking around the refrigerator.

[@tenekecop6084]

2^(-3/8) 10 -15 sec

[@felixberrisherrera8423]

Una simplificación tan sencilla que se puede resolver en 2 minutos, este profesor tardó el tiempo que duraba Albert Einstein explicando la solución de cualquier problema relacionado con la astro-fisica. Un estudiante de educación básica hubiera cambiado este video a los 6 minutos. 😮😢

[@pkchakravarty370]

Please solve the problem: x^x+y^y=31 x^y+y^x=17

[@aqwseijnhy]

(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|

[@TWJRPGGamming]

2^(-3/8)

[@НадеждаПавлова-ю3з]

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

[@superacademy247]

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

[@fd17bbd46]

​@@superacademy247or for idiots?

[@THyperon]

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

[@Budgeman83030]

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

[@CracksMeUp-182]

Sorry. It is not simplicity.

[@dziedzic-Pruski]

The eighth root of 1 is 1 but also -1.

[@albertnawab9211]

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

[@superacademy247]

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

[@adgf1x]

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

[@is7728]

(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)

[@sundaramsadagopan7795]

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

[@ლიასუთიძე]

ნერვებზე მომშლელია ასე დაწვრილებით წერა, პირველკლასელი ხომ არ უყურებს ?

[@mykhaylodorozhovets6120]

янадзвичайно довге поясненя з багаторазовим повторенням того самого.

[@actualRocketScientist]

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

[@АлександрКлевцов-ш4у]

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

[@LarbiZerguine]

Good thank you ❤❤❤❤❤❤

[@superacademy247]

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

[@DavisRimu]

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

[@harsharnjeetsingh9217]

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

[@virgilios.perdigonjr.6840]

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

[@Patrik6920]

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

[@Nikolaos.I.P]

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)

[@frankvandersteur431]

You've just failed Harvard entrance exam.

[@Mathguy1729]

Too short. I think you should use the definition of non-integer exponentiation, i.e. eˣ = Σₙ xⁿ/n! , along with the definition of natural logarithm, i.e. ln(x) = ∫₁ˣ 1/t dt, so that you can rigorously define (1/8)¹ᐟ⁸ and carefully simplify it.

[@DrBenway97]

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]

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]

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

[@keinKlarname]

Why not always = ?

[@Армен-с4н]

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

[@superacademy247]

And the better you become at Math skills 😍💕🤩

[@rameshchander2702]

Too much long procedure. Nothing told by you

[@digbycrankshaft7572]

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]

The objective is to rationalize the denominator

[@carlossummers4992]

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.

[@АйратСаляхутдинов-я4щ]

Когда тебе платят за каждую строчку...

[@macgyvertrickyman]

I dont get that k equaling 2 why two ?

[@stewarttunbridge]

I did it in my head in 5 seconds, it isn't hard. The answer is 2 ^ (-3/8)

[@adeinvest1306]

Ans = 2^(-3/8)

[@明世塵]

講解十分清晰

[@superacademy247]

Thanks 👏👏👏

[@anatolijpachomenko8280]

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

[@sharufun209]

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

[@richardchiu9975]

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

[@johnnyragadoo2414]

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]

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]

@@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.

[@clivetooth]

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

[@ibrahimbakr8788]

This solution is getting difficult for this easy problem.....))

[@l.w.paradis2108]

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