Law of Exponents - Multiplication with Like Bases

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Students will be able to conceptually understand exponents to expand multiplication involving exponents with the same base. By expanding the multiplication, students will develop the rule of adding exponents when multiplying with the same base.

Big Idea

Memorization is short term knowledge but understanding endures time. Create the rules for exponents by expanding the bases to understand.

Bellringer – Lesson Opener to Engage Prior Knowledge

20 minutes

Beginning the Activity + Homework

30 minutes

Clarifying your learning goals before beginning a lesson is very important.  To watch a short video about clarifying learning intentions and criteria for success click on the resource below. 

Clarify for students that today is focused on extending their current understanding of exponents to exponents larger than squared and cubed.  You might need to review with your class how to read exponents such as 45 which is read as four to the fifth power and ask students what this means (Look for 4x4x4x4x4).   Tell students we will be focusing today on multiplication and what happens to the exponents when both values have an exponent and you are multiplying them together.  Now is also a good time to review important vocabulary if you have not done so already.  Vocabulary such as base and exponent will be vitally important to all group discussion if your students are unfamiliar with these terms. 

Walk students through the first row of  the table, which is already completed for them as an example.  It is essential that students understand what the table is asking them to complete.  Remind students that they should be expanding the given expressions and then rewriting an equivalent expression in the far right column that hopefully uses fewer exponents if possible.  Tell students to be looking for a pattern or short-cut for rewriting these expressions without expansion because the homework page will be much faster to complete if they discover a short-cut through the activity today.  Allow students to work in cooperative groups to complete the table portion of the handout.  As students are working, move about the room providing feedback that moves learning forward.  For a short video on how to provide feedback, click on theresource below.

As you are questioning students and helping them to develop their thinking, also be selecting students or student groups who will present during the lesson wrap up session.  I like to tell each group which part of the lesson (table) they will be presenting to the class and what exact thinking I want them to share with everyone else.  Try to get a variety of thinking presented if students complete the table using different methods.

Once all or most of your groups have completed the table (about 15 minutes) hold a wrap up session lead by your student experts pre-selected by you.  For tips on holding a wrap up session, click on the resource below. 

After students present the answers to the table, allow student groups two minutes (I like to use the stopwatch on my iPhone) to complete the short-cut questions just under the table.  Then ask different student groups to read aloud their rule or short-cut for how to multiply when exponents are involved.  Use the scripting strategy to combine all the different rules into one "best" version class room and tell students to write this class rule on their papers as well.  At this point, you can pass out the unit organizer and have students add this class rule to the organizer for multiplication or save the unit organizer for the end of the unit as a wrap up review of all the rules at once.  I have used the organizer both ways and seen success either way.

For a short video on how to script click on the resource below.

Scripting Link



Once you have wrapped up the lesson and written a class rule, pass out the homework practice page and allow students to work in cooperative groups until the class period ends and the rest of the page is homework.  I sometimes post solutions to homework on my website or in because I want students to be able to check their homework as they are finishing to ensure they do not complete the entire page incorrectly.  I do not grade homework, it is practice for the unit test, so giving solutions does not affect their grade.  Also, my students have become accustom to using to ask each other for help at night with homework and it is really exciting to see them reaching out to other students about math work.  I also get on when I can and answer student questions.


Student Work Sample:

see resource below 

Teaching Strategies Employed

Several teaching strategies are employed throughout this cooperative group time.  Click on any of the following resources to watch a short video explaining each strategy:

-Activating students as owners of their own learning

-Activating students as resources for one another

-Cooperative Grouping Explained

Standards Applied in this Lesson

1 minutes

8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.


Collaboratively grouping students to become resources for one another in working through the activity to show ownership of learning brings in math practice standard one.


MP1 Make sense of problems and persevere in solving them.


Applying the strategy of mini-wrap ups that are student centered will directly bring math practice standard 3 into the lesson. 


MP3 Construct viable arguments and critique the reasoning of


Asking students to speak using correct vocabulary to explain their thinking applies math practice standard 6.


MP6 Attend to precision.


Asking students to expand expressions to see the pattern of multiplication and then reason to create a rule for performing the multiplication faster through using exponents employes two mathematical practices - one for seeing the structure of the expanded form of the expression and another for expressing the regularity of the pattern as a rule:


MP7 Look for and make use of structure.

MP8 Look for and express regularity in repeated reasoning.