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. .
@@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 Before the age of calculators, there was a good reason for doing so, but this reason is no longer valid.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.
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).
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.
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 !
= ((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
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.
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!
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).
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 !!!😮
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.
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.
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 😂😂😂😂😛😛😛😈😈😈
Ugh, this was hard to swallow! Slow mathematics (credits for this), just to get a result, that doesn't simplify, while the real solution doesn't need any calculation ( 1 / 3^(2/9) or 1 / 9rt(3²) ). To get close to the decimal result (0.78338103693727233...), I've tried some (2) manual Newton steps with a bad, but easy to calculate, starting value (1): N(x) = 7/9 x + 2/(27x^3.5) N(1) = 7/9 + 2/27 = 23/27 x = 23/27 = 851/999 = 0._851_ is still far away, so let us take a second step with some approximations: We need to calculate 7/9 * 23/27 + 2/(27 (23/27)^3.5) = 161/243 + 2/(27 x^3.5). Our greatest problem for manual calculation is this x^3.5. But we know, that x^4.5 = sqrt(x^9) ahould greater than the solution for (1/9)^(1/9), 1/3, let's say 1/2 (just a guess!). What we need, is x^3.5 = x^(7/2) approx.= (1/2) / x = 27/46. => 2/(27 x^3.5) approx.= (2*46)/(27*27) = (92/3)/243. Thus: N(23/27) approx.= 161/243 + (30 2/3) / 243 approx.= 161/243 + 30/243 = 191/243. (I've rounded down, because we expect to overshoot). This value of x_2 = 191/243 approx.= 0.786008 is a pretty good (rational) approximation...
I keep on suggesting you outline a plan BEFORE a solution is attempted. Brute force is a plan but not necessarily the best!!Remember,solving problems is a teaching opportunity. I noticed1/9 as the base and exponent. What about taking log of both sides with base 3?How about a base of 1/9?
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.
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!
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.
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.😀😀😀
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!
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.
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!
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
Unnecessary lengthy
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!
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.
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
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
= ((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
Имею плохую привычку. Начав что то смотреть, досматриваю до конца, а потомстрадаю от потерянного времени.
Me pasó lo mismo.
Chłopie, ty to skomplikowałeś, a nie uprościłeś !... przez logarytm o podstawie 3 szybko wychodzi 3^(-2/9)
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.
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
Так мало того, сама по себе задача крайне глупая.
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!
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)
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 !!!😮
Это не решение. Видимо он учился на Западе. Сразу кол ему нужно ставить в дневнике.
{(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
If it is a question of Math Olympiad then everyone would succeed in that exam....even myself.
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.
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.
You win a Fields Medal for tedium.
You make me feel like laugh 🤣. Thanks for your support and input though
There is a faster and less tedious method
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.
Is this an eye exam?
😂😂😂
One person's tedium is another person's effort to make every step perfectly clear. Very instructive.
Wow, thank you! Glad it was helpful.👌💯
a=1/9 => a^a = x => x = cln ( a * ln(a) ) => x=0,78338... => (1/9)^(1/9)=0,78338...
This answer we may get in one row by multiplying 1/9 by 3^7. Then we obtain (3^7 / 3^9)^9
Perhaps this is the first time you are teaching 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 😂😂😂😂😛😛😛😈😈😈
Alcuni passaggi ripetuti e inutili sopratutto!
Ugh, this was hard to swallow! Slow mathematics (credits for this), just to get a result, that doesn't simplify, while the real solution doesn't need any calculation ( 1 / 3^(2/9) or 1 / 9rt(3²) ).
To get close to the decimal result (0.78338103693727233...), I've tried some (2) manual Newton steps with a bad, but easy to calculate, starting value (1):
N(x) = 7/9 x + 2/(27x^3.5)
N(1) = 7/9 + 2/27 = 23/27
x = 23/27 = 851/999 = 0._851_ is still far away, so let us take a second step with some approximations:
We need to calculate 7/9 * 23/27 + 2/(27 (23/27)^3.5) = 161/243 + 2/(27 x^3.5).
Our greatest problem for manual calculation is this x^3.5. But we know, that x^4.5 = sqrt(x^9) ahould greater than the solution for (1/9)^(1/9), 1/3, let's say 1/2 (just a guess!).
What we need, is x^3.5 = x^(7/2) approx.= (1/2) / x = 27/46. => 2/(27 x^3.5) approx.= (2*46)/(27*27) = (92/3)/243. Thus:
N(23/27) approx.= 161/243 + (30 2/3) / 243 approx.= 161/243 + 30/243 = 191/243. (I've rounded down, because we expect to overshoot).
This value of x_2 = 191/243 approx.= 0.786008 is a pretty good (rational) approximation...
LOL, just put in into Wolfram Alpha, it's even better than the real N(23/27) = 0.7923865...
But this is a good approximation as well!
Okay, half of it was the correction, that I've made through rounding:
N(23/27) approx.= (191 2/3)/243 = 0.7887517...
Where are you from bro?
I'm from Kenya
Don't wrote the same expression twice...You bore me with that..
(1/9)^1/9 = 3^(-2/9) < make it simple in less than 60 sec!
I'll make a RUclips short of the same video
Fantastic way of wasting the ink, paper and time.
I keep on suggesting you outline a plan BEFORE a solution is attempted. Brute force is a plan but not necessarily the best!!Remember,solving problems is a teaching opportunity. I noticed1/9 as the base and exponent. What about taking log of both sides with base 3?How about a base of 1/9?
This is NOT an equation. It's a Math expression.. But if you let it be equal to something you can proceed.
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
Unnecessary u have exagga red many steps. 😡
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!
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
This is example of how we make our life complicated otherwise simple
nonsense . which one is faster to compute r9(9) or r9(2187)
I rationalized the denominator completely. What did I NOT do?
@@superacademy247 Can you give me please the solution How much is 1+1 = ?
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.
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!
(1/9)^1/9=
r9(1/9)=(r9(1))/(r9(9))=
1/r9(9)=1/9^1/9=9^(-1/9)=3^(-2/9)
Make the denominator rational
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 👍
You are taking all the roads to complicate rather than simplfying. It takes only two steps to simplfy it.
Show us the steps!
@@superacademy247
Simply (1/9)^(1/9) = (1/3^2)^(1/9) = 3^(-2/9)
= 3^(-(9-7)/9) = 3^(7/9). 3^(-9/9)
=(⁹√3⁷)/3
= (⁹√2187)/3
this is from
@tomctutor
t'as fais des maths?
It is very simple solution but you make it very long solution. Pls simplified it.
terimakasih. tetapi menurut saya banyak cara yang lebih simpel dan cepat...
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...?
Reply 3^-1 with 3^-2 then results is more simple!
Drag time to make RUclips clip longer.
Il complique inutilement pour arriver à un résultat encore plus compliqué !
3^7/9x3^(-9/9)=3^(-2/9)
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.
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.
Папа у Васи силён в математике.
I found 0.7733. As an approximate value of course
(1/9)^1/9=1/81
Writing same express. hundred times? Why
To emphasis and demonstrate authority over the topic
It's a litle bit complicated.
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.
Savez-vous au moins ce que signifie le symbole => ?
Более дебильного ролика не видел!
Why r u creating controversy 😮😮
I am disagree. Answer is 1/3^(2/9) or 1/ 9√9
But you should rationalize the denominator to achieve complete 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
Boring démonstration and too complicate
= (3^-2)^(1/9) = 3^(-2/9)
Or just write 1/9^(1/9)
Is also wrong... The correct result is 0.00000000258 while this gives out 0.783381...
Go through it over and over again
The question was very simple and short, but you wasted the time and paper..!!
This is laws of Indices crash course
You are passing very far!!!
Simply (1/9)^(1/9) = (1/3^2)^(1/9) = 3^(-2/9)
= 3^(-(9-7)/9) = 3^(7/9). 3^(-9/9)
=(⁹√3⁷)/3
= (⁹√2187)/3
end result is worse than initial. U still need calculator after end result
The objective is achieved. The denominator is made rational
Mmmm... the final result is not so simple...
But it gives us a rational denominator
(3^(-2))^1/9=3^(-2/9)=3^(7/9)/3 much shorter
If this is Olympiad caliber, I don’t think much of them. Are you click baiting?
Must be the marathon then...
没有任何意义，开方9次方不难吗？
When you're asked to rationalize the denominator does it make sense?
This is his way. Let's see yours.
work another 30 min to make it much complex, we are waiting
The solution is not complex. Infact the objective is achieved. The denominator is ultimately rational
Ok sorry
This is torture!!!!!
Unnecessarily repetitious....
God! It is simple!
You wasted a lot of time solving a simple question
Thanks for your feedback! I appreciate you sharing your perspective. 😎
Answer= 0.7834
Correct. But you should NOT use calculator
Using logarithm table its very eazy
Logarithm tables are NOT allowed. You should follow instructions.
😮 demasiados pasos redundantes, este ejercicio es para hacerlo más corto....esto fue muy latero
It's precision guided method to a perfect solution
НУ И РЕШЕНИЕ?! ОЧЕНЬ ГЛУПО!
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
10:42 still continue to monitor
Absolute crash course
He Teacher juan is best
Зачем это все?
In the name of Math competition 😄
@@superacademy247
Ok😀 it' a joke
Esse trem em português já é complicado agora imagina uma explicação em grego fala português.
Tenent root of power Boring....💤💤💤💤
Bunch of bs too long could have done in less steps
এই শিক্ষকের থেকে বাংলাদেশের শিক্ষকরা বেশি ক্রিয়েটিভ। (নাক বেড় দিয়ে কানধরার মতো অংক করলো)
(9)⁹ ans