Lesson 7

Practice with Rational Bases

Lesson Narrative

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 \(a^n \boldcdot b^n=(a \boldcdot b)^n\) in the next lesson (MP7).


Learning Goals

Teacher Facing

  • 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.

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.

CCSS Standards

Addressing

Glossary Entries

  • base (of an exponent)

    In expressions like \(5^3\) and \(8^2\), the 5 and the 8 are called bases. They tell you what factor to multiply repeatedly. For example, \(5^3\) = \(5 \boldcdot 5 \boldcdot 5\), and \(8^2 = 8 \boldcdot 8\).

  • 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 \(\frac52\).

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