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    1. #1
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      negative exponents

      I didn't know I had a math packet to do over the summer, so now I'm rushing to get it all done before I have my first class of pre-calc and I'm really stumped with this one problem. I need to simplify this:

      (2^-2 + 4^-2) ^ -1

      So the 2 and the 4 are both to negative exponents, then the whole thing is in parenthesis and raised to the -1 power. I tried moving the whole equation down and getting rid of the -1 exponent, like this:

      1/(2^-2 + 4^-2)

      Then I realized that the numbers underneath would have to go up, to give me

      2^2 + 4^2 = 4 + 16 = 20.

      BUT then I realized I might have done it all wrong, and needed to instead distribute the exponent outside the parenthesis. Which way is right, and if it's this second way, how do I do it?

    2. #2
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      Quote Originally Posted by Taffy View Post
      I need to simplify this:

      (2^-2 + 4^-2) ^ -1

      like this:

      1/(2^-2 + 4^-2)
      Correct.

      Then...

      PHP Code:
      2^-1/(2^2) = 1/
      and so on, which should result in 16/5 = 3.2.

      But really, use a calculator to check your work.



      As for your mistake, you can NOT simplify (2^-2 + 4^-2) into (2^2 + 4^2)^-1.
      You can only factor out the -1 power if 2 and 4 were multiplied, not added.
      Last edited by reci; 09-06-2012 at 08:53 PM. Reason: explained your mistake
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    3. #3
      Xei
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      Yeah, just translate what x^-2 means, which is 1/x^2.

      You'll get a fraction involving fractions which you can sort out using standard methods, which boil down to multiplying numerator and denominator by some number.

    4. #4
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      Great, thanks guys.

    5. #5
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      x^(-n) = 1/(x^n)

      I'll give you an example:

      5^(-1) --> x is 5; n is 1; -n is -1; so x^(-n) = 5^(-1) and

      1/(x^n) = 1/(5^1)
      1/(5^1) = 1/5 = 0.2

    6. #6
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      Always work inside parenthesis before outside. 1/(1/2^2 + 1/4^2). I got 3.2 as final answer.
      Last edited by SomethingSpiffy; 11-23-2012 at 03:01 AM.

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