This lesson, students will review the power rule, product rule, zero exponent rule, and negative exponent rule. Through student discussions, we’ll expand on students’ knowledge of exponent rules by simplifying expressions with power rule and product rule. You can expect this lesson, with additional practice, to take one `45`-minute class period.
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For teaching students how to combine exponent rules, we have broken up the lessons for students: product and quotient rule, then product and power rule, then quotient and power rule. If students are ready to combine all of the exponent rules, you can also include examples from the other linked lessons!
Start the lesson with simplifying expressions that use the power rule and product rule separately.
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To further review the exponent rules, consider asking students:
Give students two expressions that look really similar. Ask them to list down two things that are the same and two things that are different.
Give students a chance to share their ideas with each other and then call on a few students. Students are likely to bring up the differences that in one of them, the `x^4` is inside the parentheses, while in the other `x\cdot x^4` is inside the parentheses.
If students don't naturally bring this up, ask them “When you simplify the expression, will the answer be the same for both expressions?” Give them the time to simplify each expression. Ask them to write down their steps in bullet points.
Students are likely to have got different answers from each other. First talk about the order in which they would apply the exponent rules. Why is the order different in the two expressions? Make a connection to order of operations - that we need to simplify what is inside the parentheses first.
This is the first time students are combining the product and power rule. While they might know the two rules separately, they might get confused when they are combined.
In the subsequent expressions, you deliberately bring in more complications. In the first example, include `0` as an exponent. Students might be tempted to multiply the `0` and the `2` or write `x^2 \cdot x^0` as `0`.
After that, introduce an example for simplifying expressions with power rule and the product rule that includes negative exponents. You can choose to review exponent rules with negative exponents before this problem, or let students work on the problem first and then talk about negative exponents.
In this last example, you introduce simplifying expressions with product rule and power rule with numerical bases.
The key here is to systematically work through the product and power rules with negative exponents, and then apply the rule for simplifying expressions with numerical bases and negative exponents.
Students can do some practice by playing a matching activity where they match an expression with its simplified form.
Consider allowing students to work with a partner or table group to discuss their thinking as they simplify these expressions. This can allow you to circulate to listen to students’ conversations to identify and address any common misconceptions among students.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for simplifying expressions with power rule and product rule. Check out the online practice and assign to your students for classwork and/or homework!
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