Lesson 6

What about Other Bases?

Lesson Narrative

In this lesson, students use their understanding of exponent rules with powers of 10 to make sense of exponent rules for powers of other bases. Students work through problems analogous to the ones used to develop exponent rules for powers of 10. The same underlying patterns emerge, revealing the fact that the exponent rules are the same for bases other than 10. For simplicity, students do not develop general exponent rules for negative bases.

Learning Goals

Teacher Facing

  • Generalize exponent rules for nonzero bases, including bases other than 10.
  • Use exponent rules to identify (in writing) equivalent exponential expressions, and explain (orally) the reasoning.

Student Facing

Let’s explore exponent patterns with bases other than 10.

Required Preparation

Create a new set of visual displays for exponent rules that replace the base of 10 with other bases. For example, the visual display for the rule \(10^n \boldcdot 10^m = 10^{n+m}\) should be updated to a new visual display with \(b^n \boldcdot b^m = b^{n+m}\) with a guiding example that uses a base other than 10.

Learning Targets

Student Facing

  • I can use the exponent rules for bases other than 10.

CCSS Standards


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 \(8^2 = 8 \boldcdot 8\).