Skip to main content
  1. Life
  2. Education & Schools
  3. General Education

Negative fractional exponents in rational equations

See also

Suppose we have the expression (16/81)^-1/2. Remember what we do with expressions with negative exponents? We turn the negative exponent into a positive exponent, and we invert the fraction so that we have its reciprocal. Therefore, our (16/81)^-1/2 will become (81/16)^1/2. Next, we must hark back to the laws of exponents we went over in a previous article. We distribute this exponent to both the numerator and the denominator within the parenthesis. Therefore, our (81/16)^1/2 becomes (81^1/2 / 16^1/2).

Now when we have fractional exponents, we take the denominator, and use that denominator as the index of the radical expression into which we convert the expression. Therefore, 81^1/2 becomes 81 with a square root sign over it (81 is our radicand) with 2 as the index. Of course, we would not write the index in this case, because it is taken for granted that when we have a radical expression, a 2 is implied. The square of 81 is 9 and the square of 16 is 4. Therefore, our answer is 9/4.

Advertisement

Life

  • Dan Savage
    Dan Savage cares about LGBT youth, bullying and saving lives
    Today's Buzz
  • Raku
    Teachers and students can use this summer to learn a new skill
    Camera
    15 Photos
  • Beach body
    Fitness: Earn your beach body badge with bootcamp classes
    Camera
    10 Photos
  • Greek wine
    Unwind with these delicious wines: The thrilling wines of Greece
    Camera
    7 Photos
  • Mandy Moore
    Exclusive interview with Celebrity Mandy Moore concerning animal activism
    Camera
    5 Photos
  • Educational family vacations
    Find out how to take an educational family vacation that doesn't break the bank
    Camera
    9 Photos