In this lesson, students practice all of the exponent rules they have learned so far and begin to look at expressions with multiple bases. The first activity asks students to reflect on their own conceptual understanding and procedural fluency with the exponent rules they have learned so far. The second activity asks students to analyze the structure of exponents to make sense of expressions with multiple bases, paving the way towards the rule \(a^n \cdot b^n=(a \cdot b)^n\) in the next lesson (MP7).
Lesson overview
 7.1 Warmup: Which One Doesn’t Belong: Exponents (5 minutes)
 7.2 Activity: Exponent Rule Practice (15 minutes)

7.3 Activity: Inconsistent Bases (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 7.4 Cooldown: Working with Exponents (5 minutes)
Learning goals:
 Identify (orally) misapplications of exponent rules to expressions with multiple bases (orally and in writing).
 Use exponent rules to rewrite exponential equations involving negative exponents to have a single positive exponent, and explain (orally) the strategy.
Learning goals (student facing):
 Let's practice with exponents.
Learning targets (student facing):
 I can change an expression with a negative exponent into an equivalent expression with a positive exponent.
 I can choose an appropriate exponent rule to rewrite an expression to have a single exponent.
Glossary:
 reciprocal  Dividing 1 by a number gives the reciprocal of that number. For example, the reciprocal of 12 is \(\frac{1}{12}\), and the reciprocal of \(\frac25\) is \(\frac52\).
 Access the complete Grade 8 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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