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# The Power of the Power Rules in Exponential Expressions

Lesson 7 of 13

## Objective: SWBAT apply the Power Rule of Exponents to other Powers, Products, and Quotients to Simplify Exponential Expressions.

## Big Idea: Bringing it all together! Students make a decision on their plan to simplify, recognizing that the rules work if applied correctly, not necessarily in order.

*60 minutes*

#### Warm Up

*10 min*

The goal of this lesson is for students to be able to apply the Power Rule for Exponents of products, quotients, and other powers to simplify exponential expressions. Students have previously been exposed to the Power Rule of Products in Lesson 5 of this unit. In this lesson, I want students to extend their knowledge and be able to apply the Power Rule of Exponents to products, quotients, and other powers. Students should be able to apply the Power Rule of Exponents using positive or negative exponents.

My goal with this Warm Up is to introduce three problems to the students that demonstrate applying the Power Rule of Exponents to products, quotients, and other powers. I intend for this Warm up to take about 10 minutes for the students to complete, and for me to review with the class to introduce the lesson. When reviewing the Warm Up, I emphasize the power of the shortcut of using the Power Rule. I demonstrate the warm up in the video below.

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#### Guided Notes

*15 min*

After the warm up, I give students the Guided Notes for them to complete as I work through the examples with them. The purpose of today's Guided Notes is to provide students with practice with assistance on the different methods to apply to exponential expressions taken to a power. I emphasize several ways to deal with negative exponents in the Guided Notes. I also model the methods with a simpler problem at times to demonstrate reasoning of the method.

I first have students simplify the first example on their individual white boards. I instruct students to not hold up their white boards to show me until instructed to do so. After allowing students a minute or two to complete the problem. I say "Show Me." Students hold up their boards faced toward me. Then, I call on students that have simplified using different methods to explain their work to the class. I also look for any mistakes that students have made, such as adding exponents instead of multiplying them. I will have students that have incorrect answers explain their work to clear up misunderstandings. If I recognize a method that has not been used by the students, then I demonstrate it on the front board. I also post the different methods already discussed to summarize the methods. Then, I allow students a few minutes to copy the examples down in their Guided Notes.

I repeat the process above with the second example in the Guided Notes.

I think that students should be exposed to different methods, but should understand the meaning of the Power Rule and why it works in each method. I have written out the three different methods that I demonstrate or that a student demonstrates to the class in Example 1. I also have a students write out a summary about the methods used.

Here is my Summary of the methods.

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#### Independent Practice

*25 min*

The Independent Practice is for students to work on individually, and I provide the students the Key after about 25 minutes of work time. I do this to provide students feedback and a self-assessment on how well they can apply the Power Rule of Exponents. If a pair of students finish early, I allow them time to compare their work before posting the answers.

For this practice, allowing students to work individually after learning the different methods builds confidence to apply the Power Rule successfully to simplify Exponential Expressions. Simplifying Exponential Expressions is difficult for students because they have to make a decision on which method to apply based on the structure of the problem. Each student's perception of the problem when first seeing it may be different, which may result in them choosing a different method or order to simplify the problem. The students have to learn that is okay to use these different methods, and to build their own confidence and understanding of the Power Rule of Exponents. These problems can be intimidating for some students with the fraction bar, parentheses, and negative exponents and bases.

Allowing students to work without the fear of a grade provides students with a safe environment to practice, make mistakes, problem solve, and learn. Students need this practice time to develop their own sense of understanding.

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#### Self-Reflection

*10 min*

The Self Reflection is the last activity of this lesson. Students begin completing the Self-Reflection immediately after the Independent Practice is graded. This activity is focused on the ability of students to recognize which problems apply the Power Rule of Exponents to a product, a quotient, or other powers. If students better understand the structure and the math operations in the problem, it will make it easier for them to make a decision on how to simplify the expression. Students will be using reasoning (MP2) to make their decision about how to simplify the expressions.

This activity is not only a Self-Reflection for the student, I also use it as a formative assessment. The students complete the Self-Reflection as an exit slip and hand in before leaving the classroom. If time does not permit for students to complete the Self-Reflection, I assign it as homework for the students that have not completed the activity. I have provided a reflection example in the resources of this section.

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: A Penny or $100,000!
- LESSON 2: Explore the Rebound Height of A Ball
- LESSON 3: Arithmetic vs. Geometric Sequences
- LESSON 4: Linear, Exponential, or Quadratic?
- LESSON 5: The Product Rule and the Power of Product Rule of Exponents
- LESSON 6: The Quotient Rule of Exponents and Negative Exponents
- LESSON 7: The Power of the Power Rules in Exponential Expressions
- LESSON 8: Comparing Investments
- LESSON 9: Applications of Exponential Functions and Hot Cocoa!
- LESSON 10: Graphing Exponential Functions
- LESSON 11: Assessment: Presentation on Exponential Functions, Day 1 of 2
- LESSON 12: Assessment: Presentation on Exponential Functions Day 2 of 2
- LESSON 13: Scientific Notation Is An Exponential Expression