ôô

# How to Multiply Numbers with Exponents

Multiplying numbers with exponents.

By
Jason Marshall, PhD

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.

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.