Nice Math Olympiad Simplification Problem | Fraction Exponents | You Should NOT use Calculators
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- Опубликовано: 2 окт 2024
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By simplify, I think the kind teacher meant the expression should be written
with a rational denominator and in terms of n-th roots of positive integers.
So, (1/9)¹ᐟ⁹ = (1/3²)¹ᐟ⁹ = (1/3²ᐟ⁹) = 3⁷ᐟ⁹ ⁻¹ = 3⁷ᐟ⁹/3¹ = {⁹√(3⁷)}/3 = {⁹√(2187)}/3.
.
Absolutely. That is the point in this video. In other words "rationalize the denominator"
@@superacademy247 If you want a rational denominator, you must state this explicitely. Otherwise, there is no reason to rationalize the denominator. Before the age of calculators, there was a good reason for doing so, but this reason is no longer valid. For example, most people know that sqrt(2)=1.414... . Then 1/sqrt(2)=sqrt(2)/2=1.414.../2=0.707.., by an easy calculation. This was the main reason to rationalize the denominator. In the age of calculators, it makes absolutely no sense to do this.
I e
Exactly my way! I ended in 3⁻²ᐟ⁹. The last three steps I only did to validate the result.
Oui, et votre ligne de calcul est largement suffisante.
Simply you are wasting the time by repenting the trivial steps.
Ultimate way of teaching indices in one video
How is that result simpler than the original? Simplest form technically would be ²(1/9) but without using tetration, surely the simplest form would be 3^(-2/9).
Right!
I would say this is the "correct" answer
Абсурд
That’s what I got. Many steps earlier than him!
Thankyou
solving very bad..to long...
This very good for beginer, not for you ..😂.
You are right.
(1/9)^(1/9) = [3^(-2)]^(1/9) = 3^(-2/9) = 3^(7/9-1) = 3^(7/9) / 3 = root[9](2187) / 3
I have never seen such inefficiency.
It's Laws of Indices crash course
I think it is not a crash course. Rather it seems to be a brain crush course. Sorry to say, simple things turned complex unnecessarily. I am not well versed in math, still I feel so.
Unnecessary lengthy
Имею плохую привычку. Начав что то смотреть, досматриваю до конца, а потомстрадаю от потерянного времени.
Me pasó lo mismo.
You will be awarded for making a very simple math into as far lengthy and time consuming as possible.
😂🤣😂🤣
And tedious. Don't forget tedious!
= ((1/3)^2)^(1/9) = (1/3)^(2/9) = 3^(-2/9) = 3^(7/9)/3
Apart from the very exercise being quite strange, the result you came across in the end of these 14 minutes can be produced in 20 seconds or so
Похоже, чуваку просто нравится пером по бумаге водить)))
Продемонстрировал фантастическое владение степенями!
Он на Западе учился. У нас он бы и двойки не ставили. Выгнали бы
@@АурагхРамданМатфиз еще бы и пинка дали)
This is a call nay an appeal to all maths teachers. Please make your presentations shorter , avoid repetition. Your primary responsibilty , if I am not mistaken, is to make maths simpler and attractive . But many times I am forced to move away from many of the posts . A five minute presentation takes half an hour !
Yes, I fully agree with your comments.
At the end we dont know what the answer is. We gained no new knowledge of these manipulations, and we could have left it was it was at the beginning.
Чем полученный ответ, лучше условия?
“A call nay an appeal” for others to “avoid repetition”. Interesting
CANSA QUALQUER UM. COMPLICADO
Это не решение. Видимо он учился на Западе. Сразу кол ему нужно ставить в дневнике.
Chłopie, ty to skomplikowałeś, a nie uprościłeś !... przez logarytm o podstawie 3 szybko wychodzi 3^(-2/9)
What is exactly the scholar level of students who have to solve this ?
This solution is too long and if a student had to solve this during math Olympics, this would be a waste of time !!!😮
Так мало того, сама по себе задача крайне глупая.
There is a faster and less tedious method
Eu considero a resolução muito boa. A finalidade não é a rapidez de chegar no resultado final, mas sim em demonstrar o passo a passo, principalmente para os leigos, para se chegar nesse resultado.
Absolutely 💯. Thanks for recognizing that poignant fact.
Only ((3)^-2)^(1/9)=3^(-2/9)
When the index is negative you've not simplified. Make the exponent positive
3^(-2/9) = 3^(7/9 - 1) = 3^(7/9) / 3 = root[9](2187) / 3
You win a Fields Medal for tedium.
You make me feel like laugh 🤣. Thanks for your support and input though
Alcuni passaggi ripetuti e inutili sopratutto!
x= (1/9)^1/9, alors log x= (log(1/9))/9, et avec ma vieille table de logarithme de Bouvard et Ratinet (édition 1962, évidemment les moins de 60 ans ne peuvent pas connaître) j'ai la solution sans calculateur et en 15 secondes.
{(3^7)^(1/9)}/3 = 3^(7/9) * 3^(-9/9)
= 3^(-2/9)
= 1/ (3^2/9)
= 1/9√(3^2) = 1 / 9√9
Or simply
(1/9)^(1/9) = 9√1 / 9√9
= 1 / 9√9
Herr professor, if your friend did this sea of calculations and is going to give a value that needs to be calculated using a log or calculator, wouldn't it be much simpler to use the following scheme:
1) (1/9)^(1/9) = X
2) I raise both sides to the power 9
1/9 = X^9
0.111111 = X^9
X = ninth root of 0.1111111111
It will give the same value as yours, calculated, 0.78338
Hugs!
You didn't follow instructions: Calculators are NOT allowed! Thanks though for your support and input
Dear Professor, your friend must have a (serious) cognitive problem, as he did not understand my solution. I followed the rules established for the Math Olympiad strictly. Here in Brazil there is a rule that says 'mathematics is always the simplest'. I'm sorry for your difficulty in developing about ten pages of paper to arrive at my result in three lines. X = SR of o.1111111
I could stop here, but, using a calculator, I calculated the root to make sure it matched the complex solution. I'm leaving your channel. Unpleasant!
@@JPTaquari Difference between an EXACT solution and a numerical approximate solution, OK in Engineering but not pure maths,
To be pedantic, 1/9 =/= 0.1111.. (Come back and you will be forgiven).
My dear, you must have some cognitive problem. Go treat yourself, man!
Come back and see my development!
вялотекущая шизофрения....
If it is a question of Math Olympiad then everyone would succeed in that exam....even myself.
Super Academy,
A bit tedious process... (
Maybe the result here is a bit easier:
(1/9)^(1/9) = 1 / 9^(1/9) = 3^(-2/9) = 1/3 * 3^(7/9) = 1/3 * (3^7)^(1/9) = 1/3 * 3^(6/9) * 3^(1/9) = 1/3 * 3^(2/3) * 3^(1/9) = 1/3 * cbrt(9) * root(3; 9).
Here root(a; b) means a^(1/b) for a∊ℝ, b∊ℕ,
and cbrt(x) is a cube root of x∊ℝ.
What is the meaning of simplification in this case? I'm from Russia, and in our high school we have no strict rules for the result of simplification.
Not sure how this has so many views or why it was recommended to me. This is terrible work. Do not do math like this, and do not try to teach this way!
It's so many views because of the capability of rationalizing the denominator
It doesn't make sense. You only demostrated the different ways of manipulation expression rather than simplify it.
That's it. Authority on the subject.
I understand that the idea is to show how to use the different properties of powers. That's Ok. But I mean you rodount too much. I might say you show a way how to complicate something simple. Anyway, who teaches, learns.
Более дебильного ролика не видел!
This is too long and your time will run out! 😁
Check out this latest version. ruclips.net/video/dc-1v3e7tAY/видео.html
Your explanations are too long.
A demonstration of authority over the subject
It took a long period of time to solve the simple equation,you just make us confused about your simple, topic, what a good teacher. You deserved no subcriber indeed.😀😀😀
Glad it helped!
Is this an eye exam?
😂😂😂
Unnecessarily elongated. 3^(-2/3)=3^(7/9-1) 3^(7/9) /3=the result shown. No need to tread such circuitous route to reach the destination. Simplification has been turned into complexification.
It's a crash course for beginners
Don't wrote the same expression twice...You bore me with that..
This is an excellent work! there is another simple method that can be use to solve the given question. See solution to similar question here: ruclips.net/video/Ls9TWehDD0M/видео.html
Very poor method..
Why do you think so?
terimakasih. tetapi menurut saya banyak cara yang lebih simpel dan cepat...
Very very poor maths teaching,every time रिपीटेशन ।it is frustrating and boring method।please don't allow this teacher in future।
這是一個很不嚴謹而且粗糙的解，在虛數領域，1開9次方不是1，而且有9個數
But you're forgetting the fact that this is a Math expression. Your point of view is for equations! If you have something you're seeing and I'm NOT, please share.
I stopped watching this halfway through because i couldn't stand how slow he was going. You don't have to repeat every step. Its a video. If somebody can't follow then they can replay it til they can. Good god, man you're driving people away by your horrible presentation. Awful! And I like math.
original calculate ⁹√(9) at the end of these 14 minutes the solution is calculate ⁹√(2187) the solution is correct it takes 14 minutes to count from 9 to 2187 😂😂😂😂😛😛😛😈😈😈
I'm sure you could find an even longer and more tedious solution if you tried. And if this is really a math olympiad problem you wouldn't have time left for any other problems!
I found 0.7733. As an approximate value of course
Drag time to make RUclips clip longer.
Are you that desperate to make a youtube video that you would make one to waste everybody's time? C'mon man - get with the program.
Unnecessary u have exagga red many steps. 😡
এই শিক্ষকের থেকে বাংলাদেশের শিক্ষকরা বেশি ক্রিয়েটিভ। (নাক বেড় দিয়ে কানধরার মতো অংক করলো)
سلام. خیلی بد حل کردی. خیلی😅
خیلی طول میدی ، واقعا سرم درد گرفت 😢
Бред
making something out of nothing ! 9 is simply 3^2 so the question becomes 3^(-2/9) which can be written with rational denominator if desired by putting (7/9 - 1 ) instead of (2/9). olympiad? ha!
Do it here! Olympiads want to see action.
@@superacademy247 whatever that means...?
Папа у Васи силён в математике.
Catastrophic mathtically thinking !!!! Very Bad way!!
But at the end of the video the denominator is successfully rational
1/9^^(1/9)=1/3^^(2/9)=(3^^7/9)/(3^^(2/9)^3^^(7/9)=3^^(7/9)/3=(2187)^^(1/9)/3
So long
Only three steps solution like
Using unnecessary step,boring.
Perhaps this is the first time you are teaching math.
تمخض الجبل فولد جرذا عفوا
جذرا.😂
A complication problem
The solution is too long and stupid
Repite...repite y repite las igualdades.!! Interminable !
To emphasis
If this is Olympiad caliber, I don’t think much of them. Are you click baiting?
Must be the marathon then...
a=1/9 => a^a = x => x = cln ( a * ln(a) ) => x=0,78338... => (1/9)^(1/9)=0,78338...
Can you give me please the solution How much is 1+1 = ? I think you need 14 minutes video to give the answer.
When analyzing a mathematical idea it's necessary to spend time to unravel Math mystery
la brevedad es talento de genios.
este no lo tiene😅😅😅😅
Talk about beating about the bush. As a math teacher, you're really boring
Solving Math requires patience!
end result is worse than initial. U still need calculator after end result
The objective is achieved. The denominator is made rational
What a complete waste of time.
Kiding you. Too long to do nothing
Is bade solution
So complicated
Sory, this solution is so long.
Need more patient to see.
This is not a simplification but a complication
The denominator is rational. Which is less complicated
God! It is simple!
You are half mad...
Super time waste
Using logarithm table its very eazy
Logarithm tables are NOT allowed. You should follow instructions.
Too many steps
180k views 😵
Waste of time
Writing same express. hundred times? Why
To emphasis and demonstrate authority over the topic
Почему не показал как из 3^7 получил 2187?
3^7=3x 3x 3x 3x 3x 3x 3=2187
Straight forward
@@superacademy247 Это был сарказм.
Okay 👍
Nonsense
Boring
He Teacher juan is best
This is not right in exam there is time limit
This is meant only to demonstrate authority over the topic. In an examination setting even with less than a minute you're done.
USELESS
You make a simple solution look too long
Laws of indices 101
3^7/9x3^(-9/9)=3^(-2/9)
Idiotic solution for one liner.
Is it idiotic when rationalizing the denominator?
I feel wasting my time in watching this.
You are on the right channel showing you how to rationalize the denominator of big roots
No la hagas larga
WTF?
(1/9)^(1/9)=3^(-2/9)
Need a rational denominator?
3^(-2/9)=3^(-2/9+1-1)=3^(7/9)/3
Wow! It's amazing! Thanks for your input 👍💯. Nice approach to the solution.
This is a complete waste of time
Give us a formula of rationalizing the denominator without waste of time
Not a satisfactory solution
But the denominator is rational
It's a litle bit complicated.
Le résultat n'est pas plus simple que l'énoncé, légèrement ridicule.
It's simplified because the denominator is made rational
Yours is no good process, I think.
It's because that's the result required. Military grade method