Multiplying Monomials

Multiplying monomials requires that you understand and can apply the laws of exponents. Let's quickly review the laws of exponents that will be needed.

Laws of Exponents

  • Multiplying Powers with the Same Base - Add the exponents. For example:            ( a3 ) (a2) = a5

  • Power of a Power - Multiply the exponents. For example: (a3)5 = a15

  • Power of a Product -find the power of each factor and multiply. For example: (3a)2 = 9a2

When you multiply monomials, you will need to perform two steps:

  • Multiply the coefficients (Numbers)

  • Multiply the variables. (Use the laws of exponents when necessary)

Let's look at a few examples.

Each line of these examples shows a different step.

I broke it down step by step for you to see the exact process. You will be able to do a lot of this work mentally, which I will show you later on.

I wanted you to understand each step, that's why these explanations are so long.

This first example shows how you use multiplying powers with the same base in order to multiply monomials.

Example 1: Multiplying Powers with the Same Base

Multiplying monomials

This second example will utilize the Power of a Product property in order to simplify the expression.

Example 2: Using Power of a Product

Multiplying Monomials

One more example, but this time I'm not going to show each individual step. As you master this skill, this is the way in which you will multiply monomials. It's actually pretty quick!

Example 3: Multiplying Monomials

Multiplying monomials

For further help with monomials, you may want to visit our next page on dividing monomials.

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