How To Teach The Product Rule Of Exponents

Key Concepts of Product Rule of Exponents

It is important for students to discover the rules of exponents by doing an exploratory activity instead of memorizing the rules. It is much more intuitive for students to multiply the exponents when multiplying powers. An exploratory activity helps students understand why it makes sense to add the powers instead. In this blog, we talk about how you can teach students about the product rule.

How do you teach the product rule of exponents?

Step 1: Expand the expressions

Have students complete the following table independently.

When it looks like students are done, ask a student or multiple students to fill in the table on the board. 

Step 2: Write the simplified exponent form

Have students use the expanded form of each expression to write the simplified exponent form.

Step 3: Discussion

“Using the table, can we come up with a ‘rule’ for multiplying powers with like bases?”

• Allow students to talk or work together.
  • Hints you can give throughout:
    • Tell them to focus on the exponents in the original expression and the exponent in the simplified expression. How do those numbers relate?
    • Give them “a^m • aⁿ = a^?” and ask them to think about what happens with the original exponents to give us the final exponent.
• Eventually, talk through the product rule and explain how expanding each power allows us to see the total number of factors, which eventually ends up as the final exponent.
• Display the rule “a^m • aⁿ = a^m+n” on the board to be added to as the exponent’s unit continues.

Why teach the product rule of exponents this way?

Teaching the product rule of exponents this way allows students to discover the reasoning behind this rule. This creates a deeper conceptual understanding.

Vocabulary for teaching the product rule of exponents

Exponent: An exponent (or power) is a small number placed to the upper right of a base. It shows how many times the base is multiplied by itself.

Power: The power of a number indicates how many times the base number will be multiplied.

Product Rule: When multiplying powers with the same base, add their exponents.

a^m • aⁿ = a^m+n

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Misconceptions and errors students are likely to have

• Students might multiply the exponents instead of adding them.
  • Remind students of this activity. Encourage them to think about if they were to expand the powers, how many total factors would they have?
• Students may not consider the invisible exponent of 1 when a variable is written without an exponent
  • Remind them that any variable written without an exponent always has an invisible exponent of 1!

Resources

• Teacher slides to use this activity in the classroom
• Downloadable worksheet for practicing the product rule of exponents
• Quiz for assessing product rule of exponents

Frequently Asked Questions On Product Rule Of Exponents