#  >> K-12 >> Middle School

How to Get Rid of Negative Exponents in Fractions

A fraction is a way of representing one number divided by another. For example, 2/3 means 2 divided by 3.



An exponent (usually represented by a superscript or by "^") is a way of representing repeated multiplication. For example, 5^3 means 5*5*5 = 125. A negative exponent means to take the multiplicative inverse of what the same expression with a positive exponent would mean -- that is, divide 1 by the expression with a positive exponent. So 5^-3 = 1/5^3 = 1/125.

Instructions

    • 1

      Determine if the entire fraction has a negative exponent. For example, (3/4)^-5 has a negative exponent for the whole expression, but (3^-2)/(4^2)^2 has a negative exponent only within the expression.

    • 2

      Flip the whole fraction, if necessary. This step is only necessary if the answer in Step 1 is "yes." If you flip, change the sign on the outside exponent. For example, in (3/4)^-5, flip 3/4 to 4/3 and change the -5 to 5. The term becomes (4/3)^5.

    • 3

      Re-express any terms within the numerator that have negative exponents by substituting 1 in the numerator and the rest of the term in the denominator. For example, if your original expression is 2^-3/3^4, you need to re-express 2^-3. Write it as 1/2^3 and substitute that in the whole expression, getting 1/2^3*3^4.

    • 4

      Re-express any terms within the denominator that have negative exponents. For example, if your original expression is 3^3/2^-2, re-express the denominator as 1/2^2. Then write the denominator of this part in the numerator, and 1 in the denominator, getting 3^3*2^2/1 or just 3^3*2^2.

Learnify Hub © www.0685.com All Rights Reserved