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

Performing operations on exponents

See also

When two terms have variables that are raised by exponents, and we multiply these terms together, we do not multiply the exponents. Instead, we add them together. Thus, if we have x^2 multiplied by x^3, we come out with x^5. When we see two terms whose variables have exponents divided by one another, we do not divide the exponents themselves. Instead, we subtract the one from the other. Thus, if we have x^6/x^4, we end up with x^2.

We have seen before that when we add two terms whose variables have exponents, we do not multiply the exponents themselves, but instead add them. But there are cases in which we do multiply exponents by one another. (x^2)^6 would be such an example. Our result would be x^12. A similar principle is operative in cases like (xy)^9. The distributive property is used in this case, and we get the result x^9y^9. Likewise, if this exponent is applied to a fraction, such as (x/y)^9, we get x^9/y^9. The process of multiplying rational exponents is the same as that for multiplying rational numbers or fractions. The numerators of both are multiplied by one another and the denominators are multiplied by one another. So 2x^3/5 times 3x^1/2 = 6x^3/10.

Advertisement

Life

  • Tom Petty
    Seven overlooked videos that prove the genius of Tom Petty and the Heartbreakers
    Today's Buzz
  • Gaylord Pickens
    Discover Gaylord-Pickens Oklahoma Heritage Museum dollar days
    Camera
    6 Photos
  • Yoga poses
    Learn how to strengthen your core muscles with these yoga poses
    Camera
    5 Photos
  • Baby boomer STD rates
    Sexually transmitted diseases: Baby boomers booming STD rates
    Camera
    7 Photos
  • Open relationships
    Are you thinking about exercising your option to be in an open relationship?
    Camera
    5 Photos
  • Medical symptoms
    See which symptoms should cause you to seek a doctor’s attention right away
    Camera
    6 Photos