![]() Someone might make this mistake because they divide 6 by 3 and use the exponent rule for division to subtract the exponent in the denominator from the exponent in the numerator.) “Why is the equation \(2^5 \boldcdot 2^3 = 2^\), which is equal to \(2 \boldcdot 2 \boldcdot 6 \boldcdot 6 \boldcdot 6\).In this lesson, students honed their skills working with exponent rules and discovered where the rules break down when looking at expressions with mismatching bases. Here are some questions for discussion: “Why do the exponent rules we have looked at so far only work when looking at one particular base rather than mixing different bases together?” ( \(3^2 \boldcdot 3^3 = 3^5\) because there are 5 factors that are 3 on the left side, but \(3^2 \boldcdot 4^3\) isn't \(12^5\) because there are not 5 factors that are 12.).“Who can restate _’s reasoning in a different way?”.Consider involving more students in a whole-class discussion with the following questions: It is not necessary to dwell on this point since it will be addressed more fully in the next lesson. For the final question, ask students whether they think it is a coincidence that the equation is true, or if there is another, more general explanation. Ask students to share their responses and display them for all to see. This fails because with multiple bases, there are not the same patterns of repeated multiplication. ![]() The equation in the launch erroneously applies an exponent rule to a situation that involves multiple bases. The important take-away from this activity is that the exponent rules work because they capture patterns of repeated multiplication of a single base.
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