How to Raise an Exponent to a Power

Raising an exponent to a power and practice problems.

Jason Marshall, PhD
1-minute read

If you've been following along with the Math Dude podcast you'll know that we've spent a lot of time talking about exponents: What positive exponents are, what negative exponents are, how to multiply exponents, how to divide exponents, and this week we talked about how to raise an exponent to an exponent. After learning all of that you should now be able to figure out what expressions like (255)5 and ((33)3)3 are equal to. All you need to know to answer these questions is that you can raise an exponent to a power simply by multiplying the exponents. In other words, (3a)b = 3a×b for any value of the base number (i.e., the base doesn't have to be 3).

With that in mind let's take a look at the answers to this week's practice problems:

  1. (255)5 = 255×5 = 2525 (which is a really BIG number...around 8.88×1034)
  2. (42)2 / 44 = 42×2 / 44 = 44 / 44 = 1
  3. ((33)3)3 = (33×3)3 = (39)3 = 39×3 = 327 (also a really BIG number...about 7.63×1012)

Okay, that's it for now. Until next time, happy exponentiating!

Image courtesy of Shutterstock

About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.