Results 1 to 3 of 3

Math Help - Evaluating exponentiation with negative base and rational exponent

  1. #1
    Junior Member
    Joined
    Jul 2012
    From
    Earth
    Posts
    56

    Evaluating exponentiation with negative base and rational exponent

    How come

    \left( \frac {-125}8 \right )^{ \frac 23 }

    is equal to

    \frac {25}4

    I know that it can be shown using several exponent laws but I thought those were only valid for a rational exponent as long as the base is positive. I have been told that negative bases rased to rational exponents is undefined. Somebody please help me sort this conundrum out!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,385
    Thanks
    1475
    Awards
    1

    Re: Evaluating exponentiation with negative base and rational exponent

    Quote Originally Posted by MathCrusader View Post
    How come

    \left( \frac {-125}8 \right )^{ \frac 23 }

    is equal to \frac {25}4
    That really is the cube-root of a quantity squared.


    NOTE that cannot be \left( \frac {-125}8 \right )^{ \frac 3 2 } because that the square root of a negative.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2012
    From
    Earth
    Posts
    56

    Re: Evaluating exponentiation with negative base and rational exponent

    Alright thanks. I suppose if the base is negative and the denominator of the exponent is even is what causes problems. Thx again
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. multiple exponent modular exponentiation
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 25th 2012, 06:12 PM
  2. Replies: 3
    Last Post: April 27th 2011, 04:53 PM
  3. Replies: 2
    Last Post: April 24th 2010, 07:38 PM
  4. Replies: 1
    Last Post: August 19th 2008, 08:41 AM
  5. Replies: 3
    Last Post: July 16th 2008, 04:32 AM

Search Tags


/mathhelpforum @mathhelpforum