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Exploring Laws
of Exponents
Mathematical Goal: Students will investigate and discover the laws of exponents and then use
them to simplify expressions. The specific laws of exponents addressed in this activity are:
- Product Rule
- Power Rule
- Quotient Rule
- Power of a Product
- Power of a Quotient
Directions:
1. Print copies of the “Exploring Laws of Exponents” student activity sheet.
2. Have one student read the key questions out loud. Then, explain to students that by the
end of the lesson they should be able to answer these questions.
3. As a class, work through the questions pertaining to the first law of exponents. Model
how to complete the table and then do a “think-aloud” to help students understand how
to approach answering the questions that follow each table.
4. Once you have worked through the first law of exponents together, give students the
opportunity to complete the rest of the activity sheet (I typically have students work in
groups of 4 to do this).
5. When students have completed the investigation, discuss their results as a class. My
favorite way to do this is to have student groups lead the discussion (for example, I’ll
have one group discuss their findings for the power rule, another group discuss their
findings for the quotient rule, and so on).
© Julie Casola “Casola Classroom Creations,” 2015
Exploring Laws of Exponents
Name: ________________________________________________________ Date: ______________________________________ Block: ___________
Key Questions: What are the laws of exponents and how do I use them
to simplify expressions?
Product Rule
Complete the table below with a partner. Then answer the questions that follow.
Expression Expanded Form Exponential Form
1. Look at the table above. Compare the first and third column. Describe, using words, the relationship
that you see between them.
2. Use your observations from the previous question to fill in the box and complete the math sentence
below.
3. The rule you discovered in the question above is called the “product rule.” Use it to simplify the
expressions below.
a. b. c.
Power Rule
Complete the table below with a partner. Then answer the questions that follow.
Expression Expanded Form Exponential Form
1. Look at the table above. Compare the first and third column. Describe, using words, the relationship
that you see between them.
2. Use your observations from the previous question to fill in the box and complete the math sentence
below.
© Julie Casola “Casola Classroom Creations,” 2015
3. The rule you discovered in the question on the previous page is called the “power rule.” Use it
to simplify the questions below.
a. b. c. (
Quotient Rule
Complete the table below with a partner. Then answer the questions that follow.
Expression Expanded Form Exponential Form
1. Look at the table above. Compare the first and third column. Describe, using words, the relationship
that you see between them.
2. Use your observations from the last question to fill in the box and complete the math sentence below.
3. The rule you discovered in the question above is called the “quotient rule.” Use it to simplify
the questions below.
a.
b.
c.
Power of a Product
Complete the table below with a partner. Then answer the questions that follow.
Expression Expanded Form Exponential Form
© Julie Casola “Casola Classroom Creations,” 2015
(
1. Look at the table above. Compare the first and third column. Describe, using words, the relationship
that you see between them.
2. Use your observations from the last question to fill in the boxes and complete the math sentence
below.
3. The law you discovered in the question above is called the “power of a product.” Use it to
simplify the questions below.
a. b. c.
Power of a Quotient
Complete the table below with a partner. Then answer the questions that follow.
Expression Expanded Form Exponential Form
1. Look at the table above. Compare the first and third column. Describe, using words, the relationship
that you see between them.
2. Use your observations from the previous question to complete the math sentence below.
3. The law you discovered in the question above is called “power of a quotient.” Use it to
simplify the questions below.
a.
b.
c.
© Julie Casola “Casola Classroom Creations,” 2015
© Julie Casola “Casola Classroom Creations,” 2015
© Julie Casola “Casola Classroom Creations,” 2015
© Julie Casola “Casola Classroom Creations,” 2015
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