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4 solutions
This is simply a problem that generates ire more than understanding. It reminds me of the difference between -1^2, and (-1)^2 , two different distinctions. The way I read the problem, was (((2^2)^2)^2), which would result in 256. Instead, you intended the problem to look more like 2^(2^(2^2)). When all we want to do is argue about syntax, we ignore the fundamental procedures. Please, no "tricks". I could do the same with the English language: Think about how you say the word "wind" ... does it change when I give you context? ... I feel the wind blowing my hair... or ... I need to wind the clock... Context people.
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I don't make the rules. I know that − 1 2 = − 1 is distinct to ( − 1 ) 2 = 1 . Furthemore, I made a mistake with my first attempt with the tower of exponent rule, I did it like you... You make reason from certain point of view... It's like learning...
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never heard of this tower rule...would love to find it somewhere in print
Exactly! Any sot of maths needs top be explicit, otherwise different interpretations produce different results like for this example for wich i would assume is 256
Agreed. Simple Order of Operations procedures give the correct answer of 256
The way it works is actually quite simple. There are no brackets so you have to follow order of operations. Since you start with exponents, look at the question objectively. You have 2^ (2^2^2), which cannot be calculated yet, so you have to figure out the value of the exponent, thus 2^(2^(2^2)). Even the second 2 cannot be calculated yet so move to the third and then it all follows itself down. The key to doing the question is remembering that the first exponent is 2^2^2, instead of the entire number being ((2^2)^2)^2. Sorry if this is a bit confusing, it would be much easier to explain in person with a piece of paper.
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Well said. I appreciate the reply
I understand what you mean; however, the bottom line is if the author of this problem intended it to reflect the "tower rule," then it should have been clearly written to indicate the "tower rule." Instead, it's clearly written in the "power rule" form making the answer 256. With that said, I did see his comment response indicating he made a mistake.
😯 .........................
That's like the people that say you can't do certain things with 0... There are a few different definitions of zero and context matters when defining WHICH one you are using!!!
There's no point in your comparison. The way you solved it is just wrong, because of a misunderstanding of the problem. There's no need for more "context".
Now, I think people are confused with tower of exponents.
2 2 2 2 is interpreted as \Large2^\left({2^\left({2^{2}}\right)}\right) , not ( ( 2 2 ) 2 ) 2
Great solution.
how do you get that 16??????
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First the top 2 ie 2 2 = 4 .
Then 2 4 = 16.
Then 2 1 6 = 6 5 5 3 6
Even Google saids it's 256
I wish I knew how to make the numbers appear as you have, because it's exactly communicating what I was hoping to write, I just couldn't figure how to make the formating look like that :(
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You need to learn latex for that. Here is a good guide.
When you raise an exponent to an exponent you multiply those exponents, which you did in your first step down. However, when you went into your third step 2x4 does not equal 16. The end should be 2 to the eighth (2x2x2=8) power equaling 256 and not 2 to the 16th. Another way to look at it is to work from the bottom up, 2 squared is 4, 4 squared is 16, and finally 16 squared is 256. You skimpily cannot multiply the middle exponents and square it as this solution appears to be doing, because that is the only way I can see how one could get 16 for the final exponent.
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It's the tower of exponent rule , it's differet to the power of power rule...
Look at this 2 3 2 = 2 9 = 5 1 2 , 6 4 = 8 2 = ( 2 3 ) 2 = 2 6 = 6 4
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Correct. For the problem to be interoperated any other way it would have to be different I.e. have parentheses somewhere.
"when you went into your third step 2x4 does not equal 16" these are not multipliers but exponentials. So its not 2x4 but 2 multiplied 4 times 2x2x2x2 = 16
Sir, you are absolutely right
Thank you ... I will take care next time
Such a simple one
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But when power is over power then those powers are multiplied not exponential. Thats what I knew
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This is an exponent tower. You start at the top of the tower and treat the next exponent down as a normal number. After it has been worked, it becomes the exponent to the number below. This is repeated until there are no more numbers below. The final outcome is the answer.
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@James Curry – Last semester my Math professor's name was James Curry. He is black so judging by picture it's not you. #CUBoulder
2^(2^(2^2))=2^(2^4)=2^16=65536
very good explanation
thanks.your comment inspired me
2 2 2 2 = 2 2 4 = 2 1 6 = 6 5 5 3 6
2 2 2 2 = 2 2 4 = 2 1 6 = 6 5 5 3 6 . Tower of exponents rule works from top down.