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Advanced Math/College Algebra I paradox


Hi, I read your guidelines and it may seem this would fall outside the level of math you deal with, but several professors at my school, WGU, cannot seem to give me an answer I'm comfortable with.

The basic question is -2 to the second power =( i don't know how write the exponent in this form)?

I was always taught the exponent told you how many times to multiply the bases times itself, sort of shorthand for larger numbers.

Now my first response was "4", then I found out how to use my new calculator to input these problems and used this as a test because I was confident of the answer.

So I was completely shocked when the calculator returned "-4". I tried a few more time to make sure it wasn't human error and even tried Google online calculator, same thing "-4". But using those same tools, if I did it long hand, I guess you could say, -2 times -2 the answer is "4".

The math department at WGU said it could be either and repeated my question back to  me as an example. I asked how I would know which method to use they just said it depends. That's it!

To further confuse me, using () around the base -2 yields a "-4".

I love math because it is logical, black and white, at least this side of sanity, There's only one answer in math, it's universal. But this rocked my world.  

The simplicity of the numbers is not the issue, but as I progress through math this issue will always make me second guess the answer.

Thank you for any help in making my little slice of comfort whole again.

Mark V

This is a fairly basic question having to do with parentheses and the order of operations.

(-2) (-2) = 4

This is a fact. This can be rewritten:

(-2)^2 = 4

However, in the order of operations exponents come before subtraction, so:

-2^2 = -4

because first you square the 2, then you take the negative.

If your calculator says that (-2)^2 = -4, then you need a new calculator because that's wrong.

See (-2)^2 vs. -2^2.

Or for a different source: (-2)^2 vs. -2^2.

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Clyde Oliver


I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.


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