How to Multiply Numbers with Exponents

Multiplying numbers with exponents.

Jason Marshall, PhD,
January 19, 2012

At the end of the latest Math Dude article, How to Multiply Numbers with Exponents, I gave three practice problems designed to test whether or not you understand how to solve multiplication problems involving exponents. To solve these problems, you need to know that you can multiply two numbers with exponents simply by adding their exponents—as long as the bases of the numbers you're multiplying 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, without further ado, let's take a look at those practice problems and see if we can use our rule to simplify these problems?

  • 52 ∗ 55 = 52+5 = 57 ← Since both bases are the same, we can simplify the expression by adding the exponents.
  • 42 ∗ 33 ∗ 42 = 42+2 ∗ 33 = 44 ∗ 33 ← We can combine the two parts of the expression that have a base of 4.
  • 26 ∗ 42 = 26 ∗ (22)2 = 26 ∗ 24 = 26+4 = 210 ← This is a tricky one since we haven't yet learned that 42 = (22)2 = 24…but we will soon! Once you know that, all you have to do is add the exponents.