From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Basic Operations

Basic Operations

Powers

Powers, also known as exponents, are a way to shorten long strings of multiplication.

Instead of writing 5 x 5 x 5 x 5, write 5^4 which means "multiply four 5s together."

Or how about this for a timesaver: isn't 10^9 easier to write than 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10?

Important Rules of Powers

  1. Any number to the power of 0 is 1
    • 25^0 = 1 and 0.02764187^0=1
  2. Any number to the power of 1 is itself
    • 5^1= 5 and -(218)^1 = -218
  3. When you see a number raised to a negative exponent, take the reciprocal of the number (flip the fraction) and then change the exponent from negative to positive 
    • 2^-3 - (1 / 2)^3 - 1 / 8
  4. Remember to follow PEMDAS, the order of operations-6^2 and (-6)^2 are two different problems. 
    • The first, -6^2 , means to take the negative of 6^2. The answer is the negative of 36 or -36
    • The second problem means to square -6, so it would simplify as -6 x -6, or 36

People who Shmooped this also Shmooped...

Advertisement