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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 alot 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 monomials


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


Example 2


multiplying monomials example

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


Example for multiplying monomials



Need Help With Your Homework?

Enter your monomial or polynomial expression and click "simplify" to see the correct answer.






You Might Also Like These Exponent Lessons:


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