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.
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! 💖💯
@@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...
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 🤦♂️
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.
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.
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.
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.
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.
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.
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.
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!
(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.
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. 😅💯
@@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.
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!
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.💯💕🙏
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)
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.
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...)
UA-cam 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?
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.
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.
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.
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.
@@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.
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.
You are the best example of how an easy thing can be made tough 👍🏻👍🏻
I aim to make you think deeper! 😎💯Thanks for sharing your perspective! 🙏
Problem can be solved in two steps
It can be solved in one. It's 0.71 by inspection.
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.
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! 💖💯
@@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...
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 🤦♂️
@@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
🙃
2^(-3/8) is more directly
Well done.
This is not tricks, but it is a long journey trip.
It's rationalizing the denominator
Yes . Stupid long vedio for nothing
This could be solved with in only five steps.
Yes, I agree
Damaging the Reputation of Harvard University.
Lot of repeated steps.
To make everyone find it easier to understand
1/8 is 2^ minus 3. So LHS is 2^ minus 3/8. which is 2^5/8 /2 on multiplying by 2/2.
The most stupid way of solving a simple problem.You are testing the patience of the viewers.
Don't worry, you're under professional control.
@@superacademy247 What is that supposed to mean?
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.
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.
Answer is more complicated than Question ❓
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.
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.
One of the characteristis of mathematics is that it makes difficult things easy.
This actually complicates what is easy
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.
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
Very simple
(⁸√32)/2 = 1/⁸√8 is most simple and super trivial.
Stupid Harvard that you long solution man but this short
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.
Extremely boring. Writing the same thing over and over every line . It should take more than 30 secobds.
Taking more time even for simple thing to earn, I think.
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.
The simplification has yielded a complicated answer.
Not complicated because the denominator is finally rational
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.
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!
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
Much tooooo long...! 😴
Trivial. 1/8 = 2^-3. 2^-3^1/8 = 2^-3/8. Hardly difficult.
Excruciating.
Energy usurping. Brute force!
Question is simpler than answer! You made it different and more complicated!
very good, but couldnt you go further? ((2)^5/8) x (2^-1) same base, add the exponents?
I just waste 16.5 mins watching all of this while an average Asian kid can solve this problem in 15 secs
Is he amateur of Math? lhs=(2^(-3))^(1/8)=2^(-3/8).
His way is not elegant.
янадзвичайно довге поясненя з багаторазовим повторенням того самого.
1/8=2^(-3) and substitute into eq. => 2^(-3/8) = [2^(3/8)]^(-1) = [8^(1/8)]^(-1) = 1/[8^(1/8)]
(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.
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. 😅💯
Good thank you ❤❤❤❤❤❤
You are most welcome! Glad you enjoyed the video! 😁💯💕😎🙏
The final form is more complex than the given!
Why should rewrite the result of the previous equation again and again 😂
To emphasize
Sorry. It is not simplicity.
why to do all that ???
To rationalize the denominator completely
@@superacademy247 Completely..? Can it be rationalized partially..? LOL Come on man, do better...
Открыл сумочку, достал кошелёк, закрыл сумочку,открыл кошелёк, достал билет, закрыл кошелёк, открыл сумочку, положил кошелёк....
Это как раз тот случай когда из мухи делают слона...
It's a special case in which an elephant is relegated to rodent class
Foolish and unnecessary repeatation
of the same steps
Is it simplification or complexification?May I ask.
Rationalization
@@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.
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!
😂नौ दिन चला अढाई कोस ।
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
Thanks 😊🤩🤩🤩
Просто шуллер! Все мозги разбил на части,все извилины заплел!😂
Know anybody longer way to solution?
2^-(3/8) in 2 steps
This solution is getting difficult for this easy problem.....))
Let a=(1/8)^(1/8), so a^8=1/8=2^-3, so a=2^(-3/8)
Waste of time. Waste of phone battery. Nobody use in daily life.
😂You make me feel like laugh. You're hilarious 😆
It's after midnight... I couldn't sleep... I watched this over and over repeating of numbers.... chrrrr chrrrr zzzzzz.....
Take log base 2 first, then the equation transforms -3/8
Very long but patient approach.thanks sir
You're welcome 😊
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.
(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)
=(2^-3)^(1/8)=2^(-3/8)
wow, it takes hours to work one simple question ,too detailed steps makes it boring.
Sorry, you practically did nothing but time wasting
I rationalized the denominator successfully and completely
@@superacademy247And why not simply 8 ^ (-1/8)
2^(-3/8)
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
Not satisfied.
There are so many repetitions in the steps! Harvard applicants are supposed to be more intelligent than the host likes to project!
Wrost method, poor understanding of this guy....he has complicated everything, lucky we can ignore him
I've rationalized the denominator completely
You have complicated a very simple sum.
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.💯💕🙏
Почему вы так долго решаете?Устно 2^-³/⁸,не хотите так,преобразуйте,как хотите,но не так долго.
It's long because it's a crash course for newbies
So when he did the m - k and the n - k with k = 2. Was that due to the base number being 2?
You could solve this much easier and faster using exponents as verses roots.
I appreciate the suggestion! There are often multiple ways to approach a problem! 😎
For repeating the same n times, the comment is "it gives rise to" .Unnecessary repetitions.
(2^-3) ^ (2^-3) = 2 ^ (-3/8)
Done
Когда тебе платят за каждую строчку...
Alot of repetitions
It's indices 101
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)
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.
(1/8)^(1/8)=0.5Surd[32,8]=(Surd[32,8])/2 final answer
Чем больше я слушаю такие каналы, тем хуже становится мое произношение... 😢
And the better you become at Math skills 😍💕🤩
Too much long procedure. Nothing told by you
ნერვებზე მომშლელია ასე დაწვრილებით წერა, პირველკლასელი ხომ არ უყურებს ?
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...)
UA-cam 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?
@@superacademy247 I'm sorry but confusing and unnecessarily complicated is NOT fascinating or elegant.
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.
講解十分清晰
Thanks 👏👏👏
(1/8)^(1/8) = a --> a^8 = 1/8 --> a = 1/eighth root of 8. I don't think much simplification is possible.
x^8=2^-3=>x=2^-3/8.ans
(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|
Longest effort bears a very few
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.
You've earned the two marks for that question, now have you got time for the rest of the exam?
He is most stupid teacher.two line solution made confusing solution
Thanks for your support and input. Watch and learn 😎😍
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.
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.
@@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.
Пример того как не надо делать
A crash course for beginners in indices
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
Appallingly longwinded and why leave it as (2^(5/8))/2 which is not simplified when you can reduce it to 2^(-3/8)?
The objective is to rationalize the denominator
1/8^(1/8) = 1/2^(3/8) = 2^(-3/8)
Rationalize the denominator
1=
There is no maths!!!!!!!! Stop joeking
Rationalize the denominator
@superacademy247 don't Ask:simplify!!!!!!
What a foolish approach.
r u really from harvard university......i don't belive.....
Your approach Does not inspire confidence in your skills or intelligence
You mean you can't recognize the fascinating approach and style of rationalizing the denominator?
I did it in my head in 5 seconds, it isn't hard. The answer is 2 ^ (-3/8)
MIZERIE!
Ans = 2^(-3/8)
Terrible.
The denominator is completely rational
Friend such problems can be solved with the help of logarithms if not using calculators.
You Took 10 minutes to write 8^(-1/8)... Jesus
So boring !
Why not 2^(--3/8)?
Зачем двадцать раз переписывать одно и то же?
To emphasize
Perhaps interesting but certainly not a simplification.
It's simplification because the denominator is ultimately rationalized
Reign of extremely boredom ! Pl learn properly on da topic before going to teach anybody.
This is a crash course for beginners
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.
Incomplete how??? The criteria is to rationalize the denominator and I've done it. What else is required?