BadgerJelly » August 24th, 2017, 8:04 am wrote:∛2² = 2^(2/3)
At least with 1/x and x^1 I understand it makes equations easier to juggle around rather than having to write out things like 1/2/3 and instead write 2/3^1 then understand that it means 3/2.
So it is essentially a tradition?
Athena » August 24th, 2017, 10:08 am wrote: For the life of me, I could not figure out that question
Thank you for that explanation of why there are two ways of writing roots.
neuro » August 25th, 2017, 8:07 am wrote:Athena, just for your excitement, I may point your attention to the fact that the quite trivial number 1 can be written by making use of exponentials and imaginary numbers (and pi, by the way), as:
exp(π·í) = exp(π·í) = i^2 = 1
and, as a consequence, pi can be computed as
π = 4·arctan(1) = i·log(1)
This may now lead Badger to ask why the hell do we need pi if it can be indicated as the logarithm of 1 times i, but possibly this is the nice thing of maths: in the end, it is quite redundant!
rajnz00 » August 25th, 2017, 11:43 am wrote:Athena » August 24th, 2017, 10:08 am wrote: For the life of me, I could not figure out that question
Possibly because it is trite and pointless and the poser couldn't either.Thank you for that explanation of why there are two ways of writing roots.
What explanation? No matter. The answer is irrelevant.
rajnz00 » August 25th, 2017, 6:38 pm wrote:What does ^ mean?
It means "to the power of" or the opposite of root. Mathematical shorthand, without which it would become too cumbersome.
https://www.mathsisfun.com/exponent.html
The exponent of a number says how many times to use the number in a multiplication.
In 82 the "2" says to use 8 twice in a multiplication,
so 82 = 8 × 8 = 64
In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"
does not make sense to me. 8x8=64 makes sense, but why is the number 82 thrown in there?In 82 the "2" says to use 8 twice in a multiplication,
so 82 = 8 × 8 = 64
And if two 8's equal 64, what does that have to do with the number 82? 82 = 8x8=64? Huh?
No, I am not smoking pot or using LSD.
rajnz00 » August 25th, 2017, 8:51 pm wrote:Athena, 82 does not mean 8x8. It just means 82
8^{2} where 2 is in superscript is quite different and does mean 8x8And if two 8's equal 64, what does that have to do with the number 82? 82 = 8x8=64? Huh?
Two 8's does not equal 64, it equals 16 and it has nothing to do with 82, which does not = 64No, I am not smoking pot or using LSD.
Maybe you should :)
neuro » August 27th, 2017, 7:12 am wrote:
Obviously it is mathematical slang.
But it has much more sense than you realize at first sight.
If I said "8 is 8" and "8 squared is 64", then this may make some sense: if you have a room of 8x8 feet you have 64 square feet (8x8, 8², 8^2)
And if the room is also 8 feet high, then you have 8x8x8=512 cube feet, so I could say 8 cubed is 512. And I shorthand write it as 8^3, 8³.
Then you may have noted that mathematicians do not stop in front of anything, so they say if it makes sense to talk about 8 squared = 8x8 = 64 = 8² = 8^2, and 8 cubed = 8x8x8 = 512 = 8³ = 8^3, why shouldn't we be able to write 8x8x8x8x8x8 = 8^6, and why shouldn't we be permitted to write 8^0.2, or 8^(1/2) or 8^pi?
So they did. Computing 8^pi actually is not so trivial, but there is a way (or actually a number of ways), such as computing the exp(pi·log(8)), or, if you are content with an approximation, taking a mathematical ruler (did you ever see one? they are magic!), measure the distance between 1 and 8 on the, multiply it times 3.14, and look for the number on the ruler that is located at such distance from 1.
Athena » August 26th, 2017, 3:28 am wrote:
Okay, and what does "to the power of" mean?
How do you get that little 2....?
Athena » August 30th, 2017, 11:42 am wrote:I understood "to the power of" means "multiplied by itself"
I have strange notions and more imagination than knowledge and something really awful happens when I try to understood math.

neuro » August 31st, 2017, 3:25 am wrote:Athena:
in some computers and operative systems you hit number 2 while holding down the "AltGr" key and the small 2 up there appears.
Otherwise, you open word and look for the character menu, choose "superscript", and the following letters will appear smaller and displaced upward.
On this forum you can obtain it by hitting the "sup" button and writing the "2" between the [ sup]and[ /sup] tags that magically appear in your writing box: here > ^{2}
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