How to Divide Numbers with Exponents

More examples of dividing numbers with exponents.

Jason Marshall, PhD
1-minute read

At the end of the latest Math Dude article, How to Divide Numbers with Exponents, I gave three problems to help you practice solving division problems containing exponents. To solve these problems, you need to know that you can divide two numbers with exponents by subtracting their exponents—as long as the bases of the numbers you’re dividing are the same! In other words, this rule says that:

2m / 2n = 2m–n

The letters “m” and “n” here stand for any exponent whatsoever. And remember that the base doesn’t have to be 2 for this equation to work—it can be anything.So now let's take a look at those practice problems and see if we can use this rule to simplify them:

  • 55 / 52 = 55–2 = 53 ← Since both bases are the same, we can simplify the expression by subtracting the exponents.
  • 42 ∗ 33 / 42 = 33 ∗ 42–2 = 33 ∗ 40 = 33 ← We can combine the two parts of the expression that have a base of 4. Also, as we'll learn in this week's episode, we see here that any number raised to the 0th power is equal to 1.
  • 26 / 42 = 26 / (22)2 = 26 / 24 = 26–4 = 22 ← This is a tricky one since we haven't yet learned that (22)2 = 24 (although we did see it in last week's practice problems). But once you know that part, all you have to do is subtract the exponents.

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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.