Japanese | Math Olympiad | A Nice Algebra Problem
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- เผยแพร่เมื่อ 16 ต.ค. 2024
- Hello My Dear TH-cam Family 😍😍😍
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It takes about eight seconds to see that that's 2^18.
Definitely not an Olympiad level problem.
Yeah, pretty obvious that the one and everything past the one goes away immediately
Now solve that in your head. I got 262144 from 512^2
I know the powers of two instantly from direct memory up through 2^16, but I usually then have to calculate a bit. I've just never bothered to learn the higher powers. I spent my career working in the digital hardware area, but by the time powers higher than 65536 started to become "more relevant" I had moved on to other facets of the work, so those beyond 16 just never got "burned in" like the lower ones did.
I can give them all to you in hexadecimal, though. 🙂 0x40000. There's a reason we made so much use of hex.
@@KipIngram I'd bet you know 2^20 (one MB)
for computer person - after you get to 2^18 = 2^10 ( 1K ) * 256 - multiply that - easier than all that stuff after 2^18 in this video. Or 2^18 =- 2^20 (1M ) /4. both give the correct answer and easier.
It's easier to multiply 2¹⁶ = 65.536 with 4.
The exponentiation is not associative: usually when we write in the canonical up- indexed way a^b^c we conventionally intend (a^b)^c= a^(bc) and not a^(b^c) ; the same convention extends for multiple exponents if wrote without paranthesis:a^b^c^d= ((a^b)^c)^d= (a^(bc)) ^d=(a^(bcd)) and so on. Thus in this case we should obtain the square root of 2^(540)=2^270; In the other hand, this solution uses the opposite convention, i.e. square root of 2^(6^(2^(1^(5^9))))=square root of 2^(6^(2^(1)))= square root of 2^(6^2)=square root of 2^36=2^18
Obviously the correct answer is 2^270
oml bruh you can straight up cancel out the 1^5^9 and get sqrt(2^6^2) = 2^18 its that simple dont overcomplicate things take it easy
They're just going step by step for novices who might not see it as quickly. There's other channels for more advanced math stuff.
YES!
I think this problem is more interesting if instead of solving for the square root of 2^6^2^1^5^9 you solve for the square root of 2^6^2^1^4^4 which has an answer with same digits as the problem
Is there any need after final square root is done?
It's 2 multiplied many times by 2.
2*2*2*2...*2
If you sqrt() it it's just sqrt(2) to the power what is written as the exponents. Just write the sqrt sign around the number two.
Zebras and 🦒 giraffe are having some positive corelation 😃😄😁😄😃😃😃
In this exponential problem, the exponent 1 does not represent a unit in the base 10, but an exponent of the base, and thus it is one factor in the hierarchy of exponents which are multiplied to find the total exponentiation. The step of asserting that 1 to the (5x9) power =1 is an invalid step. So as others have noted, the correct answer is 2^270. That is, the answer is [2^(6x2x1x5x9)/2]
Before watching:
Alright, if you have like a^b^c^d^e^f^g, you'll typically calculate f^g first, then e^(f^g), then d^(e^(f^g)), and so on,.
With that in mind, we can ignore the outermost 3 exponents we see. Why? Because those last 3 are 1^(5^9)), and 5^9 is a real number, and 1^X = 1 for real X.
So what this actually meansi s that we're looking at √ 2^(6^2). But square root is simply an exponent of 1/2.
Thus, √(2^(6^2)) = (2^((1/2)6^2)) = 2^(36/2) = 2^18.
Solution is 2^18. Because we're not solving for X, but simply evaluating a square root, we do not include the negative root in this case.
Most math classes will allow you to leave the term 2^18 as-is. However, if your class is currently doing a unit on *evaluating* exponents, you may have to multiply it out. Quickest way without knowing the higher powers of 2 (suppose you only know as far as...2^12 = 4096) would be to do (2^9)(2^9) = 512*512
= 1024
+ 5120
+256000
= 262144
Honestly 4096*64 is probably going to go faster, but I went with what popped into my head.
I am sorry but (a^m)^n = a^(m.n). Hence, we will have: 2^(6.2.1.5.9) = 2^540. With the square root, we will have: 2^270. When you make 1^(5^9) = 1, you are omitting that the real expression is X^1^59 where X is 2^6^2. The final result is still 2^270.
@@CBressanPhoto Not quite.
See, you're attempting (a^m)^n = a^(mn). While that property does hold true, it doesn't apply here until our final step, because we don't *have* (a^m)^n until the final step.
Each exponent here acts as an exponent *on the previous exponent* . Until the very last step we're not doing (a^m)^n, we're doing a^m^n, or if you want to make the order of operations more clear, a^(m^n).
When dealing with nested exponents, you do the rightmost terms first. So we first do 5^9, then 1^(5^9), then 2^(1^(5^9))), and so on.
Therefore, when we get 1^(5^9), we know that equals 1, so we have 2^(6^(2^1)) = 2^(6^2) = 2^36. We then take the square root of this term, which is an exponent of 1/2, and apply *that* as per (a^m)^n rules (because the square root is applied to the whole expression, not to an individual exponent). That gives you 2^(36/2) = 2^18
Addendum: To clarify, the issue is how we are showing the exponents.
In the video, we're shown stacked numbers, *not* carats ( ^ ). With stacked exponents, the convention is unambiguous; right-to-left.
With carats ( ^ ), things get ambiguous. Thus, in cases like this, carat notation should be avoided wherever possible. However, we're stuck on TH-cam, and I don't *think* we can type out a number with 6 stacked exponents in the comments here *without* using carats.
To summarize:
Stacked exponents: Use the method I showed, right to left (so 5^9 first, then 1^(5^9), so on and so forth).
Carat ( ^ ) notation: Ambiguous. Either method is justified; therefore, this sort of terminology should be avoided due to the ambiguity.
Wrong solution..the powers should be multiplied an not rooted...andswer is 2^270
I get this to be 64 ie 2^6
Forget about the top three numbers. One to the power of anything equals one.
А как вам такой вариант:
1^5^9=х=1^(5^9)=1
2^х=2^1=2
2^6=y
тогда получается
(у^2)^½=у=2^6=64
Что скажете? ❤
2^(0,5*6*2*1*5*9) =2^(270) - i guess - i was wrong and rely bad at math and al those u-tube commies r foking geniuses///
Why is everyone thinking of 2^18 , I think its 2^36 , since there is whole underroot therefore it will be 9^(1/2).
x^(n/k) = ᵏ√xⁿ ; x ≥ 0
9^(1/2) = ²√9¹ = 3
√2³⁶ ≠ 3
√2³⁶ = 2¹⁸
= 2¹⁶ · 4
= 65.536 · 4
= 262.144
Forget powers of 1: result is always 1. 2 power 1 is 2. 6 power 2 = 36. But you are in a square root, and a square root of any number power 2 is this number. Then, square number of 2 power 36 is 2 power 18. Then, the result is 2 power 18 = 512 x 512
Piece cake!
Math olympiad level ? I cannot believe it.
U COMPLICATED IT MORE...
Just put 2 in place of 1 and see the magic of infinity.
CM Maan is right.Needs reelection for
Parliament.
great job thanks
The important point is to ‘notice’ 1 in power. Else, you will complicate
2^18
The key is you need to recognize that 1
2
6
2. =(2⁶)²is it right or wrong.
U can solve without assuming 5^9=x one sight easy question
How 2 power 6 power 2 can be 2 power 36. Power get multiplied so it should be 2 power 12 rather than 2 power 36. Sq root of it will be 2 power 6.
Wrong-you perform successive exponentiations from the top down. 2^6^2 should be interpreted as 2^(6^2), or 2^36. The square root of that is then 2^(36/2) = 2^18.
Please note. I was in error. Mea culpa. In hindsight I wish I'd stood on my desk and shouted LIAR! to any math teacher who told me categories in PEMDAS are always, always, always evaluated left to right in absence of parentheses.
Exponentiation is evaluated right to left.
I'll leave my comment below to document what I'm talking about. Please understand my statement below is wrong.
@@ThreePointOneFou Are you saying that 2^6^2 is not the same as 2^12? Even in this video a^b^c is represented as the same as a^(b*c).
Evaluate exponentiation from the bottom up. Otherwise 2^6^2 is 2^36 and not equal to 2^(6*2).
@@johnnyragadoo2414 Successive exponentiations are supposed to be evaluated from _right_ to _left_ when written horizontally, to reflect the top-down rule that applies to exponentiation. (Ideally, exponentiation wouldn't be written like that, but those are the limits we're stuck with in commentbforums without mathML or similar support.) The problem shown should be evaluated as though it were written 2^(6^(2^(1^(5^9)))).
@@ThreePointOneFou Then 2^6^2^1^5^9 wouldn't equal 2^(6*2*1*5*9).
As it shows in the video, a^b^c = a^(b*c).
So, which is it? Should a^b^c = a^(b*c)? I think it should.
Correct, 2^6^2^1^5^9 is not equal to 2^(6*2*1*5*9). And no, a^b^c should be evaluated as a^(b^c).
The video does everything correctly, apart from a bit of slightly sloppy writing when showing the rule that (a^b)^c = a^(b*c).
When evaluating exponents, the exponent must be fully determined before raising the base to that power-in other words, 6^2^1^5^9 must be calculated _before_ raising 2 to that power. Thus, 2^1^5^9 must be calculated before raising 6 to _that_ power, meaning 1^5^9 must be evaluated before raising 2 to _that_ power, etc. In other words, exponents must be calculated from the top down, or from right to left in horizontal notation.
√(2^36) = (√2)^36 = 2^18 = 4^9 = (4^3)^3 = 64 * 64 * 64
In 5 sec, i get the answet 2^18
The key is number 1
Good
First learn the basis of math, THEN try and post this video again...
correct, please!
2^9×2^9 = 4^9 = 4^5×4^4 = 1024×256 = *262144* 💪🤙🏆🤣🇪🇺🇨🇭🇮🇹🇪🇸
Equals 1.
The actual video is to find the value of 2^18
It would have been nicer if it came out to 262159
Koi power ke upar power hoti hai toh usse multiple krta toh koi usse base power jaise treat krta hai
🇰🇭🇰🇭🇰🇭🇰🇭🇰🇭🇰🇭🇰🇭🙏🙏🙏👍ល្អណាស់ good👍
I solved and found 2^18 in 5 seconds
10 seconds to 2^18=262144. Yes I know my powers of 2 by heart
@@johnnyragadoo2414 1 ^ 2 ^ 9 = 1. 2^9 is even, 9^2 is odd. You just fooled your maths completely
@@johnnyragadoo2414 ln(1+2+3)=ln(1)+ln(2)+ln(3) is a singularity, not a démonstration ln is associative. 2^4=4^2 is also a singularity, not a proof power is commutative
@@johnnyragadoo2414 10^4^2=10^16=10000000000000000 Did you write ANYTHING correct?
@@johnnyragadoo2414 back to the question, you have a 1 in the ladder of powers, therefore you must ignore what comes after. 2^6^2^1= 2^6^2=2^36. Apply square root, 2^(36/2)=2^18=262144
@@johnnyragadoo2414 You must read power from right to left 1 ^ 5 ^ 9 = 1 ^ (5 ^ 9) = 1. Result 262144. Period. And if you want to change the rules of math, try with prime numbers and figure out (2^3)^5 and 2^(3^5) are not the same. Result 262144
Parabéns! Complicado NÃO, extenso! Longo! Tem como fazer menos Longo?
512*512 using quadratic equation is funny. Maybe you know ANOTHER way to multiply numbers? 😂😂😂
2^18
Пояснення не правильне, відповідь 2^270
Если 1^а=1, то 5^9, вообще не играет роли и не зачем уделять внимание ей
Yeah that’s what I figured. Lol.
MY calculs does 513...
And not so longtime and complicated...
cool
this music is from electrolab channel
❤❤❤❤❤❤❤
8
Square root from 262144 is 512. The final answer 512.
2の270乗じゃないの？分からん
What about 29=x
Hic est 2^18 responsum.
Song name plz ? ❤
La tete vide by BERTYSOLO
Ну там же есть 1 среди степеней, начиная с неё можно просто все стереть. Остается √2³⁶ = .....
it is 2^18
No, it's not. It's 2^270. Exponents are not associative. They can be rearranged, but not regrouped.
WRONG!!!! Random multiplication of exponential is not allowed
It is really not that difficult to just multiply 512 x 512.
Yes - takes a few seconds to do in your head.
64
2 power 270
Not the right answer.
Did you do it right? You work from the top down. You'd calculate x = 5^9, and then 1^x. But that will just be 1, because 1^ is 1. Then we have 2^1, which is 2. Then 6^2, which is 36. Then 2^36. Then we take the square root of the whole thing, which is 2^18.
You do not start at the bottom 2 and work your way up.
The answer is 2^18.
No !!!!!!!
Quan fas (1⁵)⁹, dius que és igual a 1 i no és cert !!!!!
Tractes l'1 com si fos Base i no ho és -----> és un exponent!!!
No és correcta
El correcta és
V(((((6)²)¹)⁵)⁹)=
V6⁹⁰= 6⁴⁵
Непросто не пойти за всеми! ❤
2^18😅
Full error, answer incorrect! This lie
😮
All wrong. The result is 2^540
2 power x
xdd it takes like 1 second to see the answer sqrt(2^36) = 2^18
262 144
Meh ... took me less than 5 seconds.
))))))
2^(18)
1
E o 5^9 ?
2¹⁸
19
too easy!
Was this olympiad for 4th graders? It is ridiculous to spend 6.5 minutes on this stupid problem
Es correcto
I got a result 2^18
Before i watch the result
@@bmkdz Same here. Took about eight seconds looking at the opening screen. The 1^5^9 just goes away.
👍😊🇺🇸✌️
Please speak rather than adding useless music, try to verify the source and having something challenging will help people.
Trur❤
No, on the contrari, Music is better than talk
no problem but idiocy
Nice trick
It’s 262144
262144
太吓人了，简单的很：32.
buy a stylus please!!!
Can we PLEASE stop with the common core bullshit? These competitions don’t give time to do all of that extra bullshit
Annoying music
Its boring. Could have been shortened.
2^18
29
2^18
2^ 18