Author Topic: Exponents  (Read 12222 times)

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Offline metrologistTopic starter

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Exponents
« on: April 09, 2019, 01:00:25 am »
What is the answer to this?

-34
 

Offline Nusa

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Re: Exponents
« Reply #1 on: April 09, 2019, 01:15:27 am »
What is the answer to this?

-34

  -81
 

Offline metrologistTopic starter

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Re: Exponents
« Reply #2 on: April 09, 2019, 01:39:37 am »
Well, the question was why isn't the negative considered in the calculation. It seemed obvious if one says y=3x-34, but not so much when you mouth minus three to the fourth. It sounds a lot like the square root of minus two. How would you mouth that properly? Minus two to the point five? But what if you wanted to actually say square root?
 

Offline Nusa

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Re: Exponents
« Reply #3 on: April 09, 2019, 01:51:48 am »
It was considered in the WRITTEN calculation, using the traditional order of precedence, and you got the entire answer you asked for.

Verbally, you need to make clear the order of operations in some manner.

Minus three to the fourth vs The negative of three to the fourth.

Square root of minus three vs negative square root of three.


 

Offline Buriedcode

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Re: Exponents
« Reply #4 on: April 09, 2019, 01:59:48 am »
Consider x4.  If x = -3 then the answer is 81.  If the equation was -x4  and x = -3 then it would be -(x4) or -1 * x4  = -81.  In that second instance because the exponent is even, the answer would be -81 for x = 3, or x= -3.  Brackets are important and I do see them left out of equations fairly often.
« Last Edit: April 09, 2019, 02:01:34 am by Buriedcode »
 

Offline MyEEVBlogAccount

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Re: Exponents
« Reply #5 on: April 09, 2019, 02:04:20 am »
It is because operators have a property called "precedence."  Precedence, sometimes called "binding strength" or "binding level," determines the order that the operations are done.  In mathematics, the exponentiation operation is done before any addition (and, by extension, subtraction) operations are done.  Now, negation is actually considered to be subtracting the number from zero.  So, -3**4 is actually (0 - (3**4)) when you put in the parentheses sets to disambiguate.

Now, why the operators are evaluated in that order is a more complicated, due the need to understand their iterative nature, and need to understand identity elements and inversion elements.
« Last Edit: April 09, 2019, 02:10:46 am by MyEEVBlogAccount »
 

Offline metrologistTopic starter

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Re: Exponents
« Reply #6 on: April 09, 2019, 02:14:52 am »
Yes, thanks all. I see no reasonable solution to my problem.
 

Offline Nerull

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Re: Exponents
« Reply #7 on: April 09, 2019, 02:27:49 am »
The reasonable solution is to pay attention to order of operations and use parenthesis where needed. I'm not really sure what about that is too difficult.
 

Offline MyEEVBlogAccount

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Re: Exponents
« Reply #8 on: April 09, 2019, 02:29:24 am »
I think I read past your real question my first time reading.  I would say something like "what is the negation of three to the power of four" and "what is the negation of the square root of three," respectively.  Although, I did have a professor in graduate school who insisted you included the zero and parentheses and say something like "what is zero minus the quantity of three to the power of four."  Ether way, saying "negation" makes it more clear what you are doing and sounds more like -(3**4) than using the word "minus."  It does to me anyway.  Perhaps the compromise of "what is the negation of the quantity of 3**4," is the right way to go on ambiguity.
« Last Edit: April 09, 2019, 02:36:22 am by MyEEVBlogAccount »
 

Offline Brumby

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Re: Exponents
« Reply #9 on: April 09, 2019, 02:37:31 am »
The reasonable solution is to pay attention to order of operations and use parenthesis where needed. I'm not really sure what about that is too difficult.

Indeed.  The rules have been set out for quite some time now.  There is NO ambiguity in what was written.

If there IS an issue with the expression, then that lies with the person who prepared it.  THAT is, actually, a much more important step than resolving it.  If it is not written correctly, then you will not - and can not - get a correct answer.
 
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Offline CatalinaWOW

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Re: Exponents
« Reply #10 on: April 09, 2019, 02:49:43 am »
Yes, thanks all. I see no reasonable solution to my problem.

Nusa gave a good answer.  The problem is that language is less precise than written mathematics.  If you can't write it down you have to get verbose to get the same level of precision.

Another way to get the verbal precision -Spoken RPN.  4, Enter, 3, Enter, X^Y, CHS.  Again verbose, but that is the price you pay.  Writing it down solves the other problem.  The listener often cannot keep track of the verbage required for precision.
 

Offline Wimberleytech

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Re: Exponents
« Reply #11 on: April 09, 2019, 02:56:47 am »
If a chicken and a half lays an egg and a half in a day and a half, how long does it take for a chicken to lay two eggs?
 

Offline 0culus

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Re: Exponents
« Reply #12 on: April 09, 2019, 02:57:21 am »
Well, the question was why isn't the negative considered in the calculation. It seemed obvious if one says y=3x-34, but not so much when you mouth minus three to the fourth. It sounds a lot like the square root of minus two. How would you mouth that properly? Minus two to the point five? But what if you wanted to actually say square root?

Think of it like this: $$0-3^4 = 0-81 = -81$$

There's no square root of -1 involved.

(yes you can in fact embed LaTeX in the forum!)
 
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Online tggzzz

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Re: Exponents
« Reply #13 on: April 09, 2019, 07:48:35 am »
Consider x4.  If x = -3 then the answer is 81.  If the equation was -x4  and x = -3 then it would be -(x4) or -1 * x4  = -81.  In that second instance because the exponent is even, the answer would be -81 for x = 3, or x= -3.  Brackets are important and I do see them left out of equations fairly often.

There were no brackets, so using the normal laws of arithmetic the answer is unambiguously -81.

Isn't BEDMAS taught any more? (Brackets, exponents, division, multiplication, addition, subtraction).

Of course if non-normal laws are being used, the answer can be anything you want; see APL for some interesting examples :)
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Offline Zero999

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Re: Exponents
« Reply #14 on: April 09, 2019, 08:41:50 am »
Yes, thanks all. I see no reasonable solution to my problem.
Perhaps you meant this:
(-3)4 = 81
Note the brackets!

I've also seen using superscript for the minus, but don't know whether it's correct or not.
-34 = 81

Everyone who's posted above is right: -34 = -81
 

Offline soldar

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Re: Exponents
« Reply #15 on: April 09, 2019, 08:48:35 am »
Yes, thanks all. I see no reasonable solution to my problem.

What's your problem?
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Online tggzzz

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Re: Exponents
« Reply #16 on: April 09, 2019, 09:13:12 am »
I've also seen using superscript for the minus, but don't know whether it's correct or not.
-34 = 81

It isn't correct for normal arithmetic/maths.

In APL "high minus" is normal notation for a negative number (i.e. part of the number itself), with minus being reserved for the subtraction operation. I've heard "high minus 3" pronounced "neg 3".
https://en.wikipedia.org/wiki/APL_syntax_and_symbols
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Offline Datman

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Re: Exponents
« Reply #17 on: April 09, 2019, 09:45:31 am »
If you write -3x , it should be negative independently on x. The sign can not depend on x even or odd!
 

Offline taydin

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Re: Exponents
« Reply #18 on: April 09, 2019, 10:04:31 am »
If a chicken and a half lays an egg and a half in a day and a half, how long does it take for a chicken to lay two eggs?

Infinity ... Chicken in our world aren't linearly scalable, so if you cut off 1/3 of the "one and a half chicken", you'll get a dead chicken  ;D
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Offline soldar

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Re: Exponents
« Reply #19 on: April 09, 2019, 10:50:28 am »
If a chicken and a half lays an egg and a half in a day and a half, how long does it take for a chicken to lay two eggs?

Infinity ... Chicken in our world aren't linearly scalable, so if you cut off 1/3 of the "one and a half chicken", you'll get a dead chicken  ;D
Chickens don't lay eggs. Hens lay eggs. Chickens lay drumsticks.

Half a chicken lays dead. In a supermarket. For $5.25 a pound.
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Offline Wimberleytech

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Re: Exponents
« Reply #20 on: April 09, 2019, 11:26:08 am »
Quote

Isn't BEDMAS taught any more? (Brackets, exponents, division, multiplication, addition, subtraction).


We use the mnemonic: Please Excuse My Dear Aunt Sally
« Last Edit: April 10, 2019, 11:53:03 pm by Wimberleytech »
 

Offline ebastler

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Re: Exponents
« Reply #21 on: April 09, 2019, 11:44:12 am »
Yes, thanks all. I see no reasonable solution to my problem.

It is really simple. Due to the operator priorities which are agreed upon in mathematical notation, -34 = -(34) = -81.

If you were thinking of (-3)4, then that's what you have to write, including the parentheses. And that would evaluate as (-3)4 = 81.
 

Offline Brumby

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Re: Exponents
« Reply #22 on: April 09, 2019, 02:38:48 pm »
If you were thinking of (-3)4, then that's what you have to write, including the parentheses. And that would evaluate as (-3)4 = 81.

This is exactly my point here:
If there IS an issue with the expression, then that lies with the person who prepared it.  THAT is, actually, a much more important step than resolving it.  If it is not written correctly, then you will not - and can not - get a correct answer.
 
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Offline Andrew Morton

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Re: Exponents
« Reply #23 on: April 09, 2019, 02:55:47 pm »
The - is part of the number, not an operator, so it's the same as -3 * -3 * -3 * -3.
 

Offline ebastler

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Re: Exponents
« Reply #24 on: April 09, 2019, 03:02:13 pm »
The - is part of the number, not an operator, so it's the same as -3 * -3 * -3 * -3.

Wow - it's brave to claim that, after about ten people have stated the opposite.  ;)
And I'm afraid it is wrong: https://en.wikipedia.org/wiki/Order_of_operations#Unary_minus_sign
 
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