Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test

Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator

Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets
» » Laws of Exponents

Using the Laws of Exponents

Before you begin working with monomials and polynomials, you will need to understand the laws of exponents. There are three laws or properties that I am going to discuss in this lesson.

We will look at the following properties:

  • Multiplying Powers with the Same Base

  • Power of a Power Property

  • Power of a Product Property

For each of the three laws, we will write a few examples in expanded form. This will help you to understand why the law works. The I will define the property. Finally we will look at a few examples.

Ok... let's get started!

Multiplying Powers with the Same Base

laws of exponents


When a term does not contain an exponent, it is assumed to be 1.

For example:

3 = 31        y = y1        r = r1

Power of a Power Property

power or a power property for laws of exponents

I know that these properties can be confusing. If you need direct video instruction, check out the Algebra Class E-course.

Power of a Product Property

Before we start this one, let's define the word product.

A product is the answer to a multiplication problem.

So, power of a product means that we are raising a multiplication problem to a power. Take a look at this example:

power of a product property

Those are the only three properties that you'll need to remember for this unit! As you complete the practice problems below, refer back to the properties if needed!

Practice Problems

Directions: For each problem identify the property used. Then simplify to lowest terms.

laws of exponents practice

Answer Key

laws of exponents answers

Great Job! Now let's move onto learning about monomials!

You Might Also Like These Exponent Lessons:

Like This Page?


We would love to hear what you have to say about this page!

Top of the Page

Follow Algebra-Class

Algebra Class E-course Members


Sign Up for Algebra Class E-courses

Click here to retrieve a lost password.

Search This Site

Custom Search

Having Trouble with Your Homework?


Algebra Class Courses

algebra ecourse

algebra 1 review course

pre algebra ecourse

Algebra Class
Most Popular Pages

algebra practice test

algebra cheat sheets

algebra formulas

What People Are Saying...

Dear Karin,

I am a homeschool mom of five who struggled with finding a solid algebra program for my older boys until I came upon your algebra class. Your tutorials are straight forward and detailed. Your assignments are designed in such a way that we can spend extra time on what my children need to and move on when they understand something more easily.

I am a math-lover myself and am excited that you have finished part 2 of this course. My boys are understanding algebra in a way that they never were able to with other courses due to the detail and care that are in each of your lessons. I also appreciate that you are available to answer questions.

Thank you,

Jacqui Coleman

Dear Karin,

Finding your site was such a blessing to me! I have been out of school for 13+ years and finding out that my next course would be Algebra scared me to death!

I have now found a new love of learning for algebra--something I never thought would happen. After indulging in the section of functions, I decided to explore other areas that I have just learned. It made areas such as inequalities and graphing so much easier to grasp!

I just wanted to thank you for your passion and dedication for helping others! I also love the fact that you add in some humor, too. I have shared your site with classmates and hope they take an opportunity to look into it as well! Thank you----

With greatest respect,


Hi Karin,

I just spent 3 hours doing Unit 5 Lessons 1 & 2 because that is what I am learning at school this week, and cannot believe my progress. I so wish I would have found your course sooner. It is amazing. You explain everything in such clarity it's like night and day. Thank you so much for getting me started. I am so happy you can't believe it. You are the best instructor ever!

Thanks again.


Connect and Follow Algebra Class

Copyright © 2009-2015 Karin Hutchinson ALL RIGHTS RESERVED