Unit 7, Lesson 3
Powers of Powers of 10
Grade 8
Preparation
Lesson Narrative
In this lesson, students make use of repeated reasoning to discover the exponent rule . Students begin by computing the volume of a very large cube. Next, they expand expressions written as a value with an exponent raised to another power and notice patterns when asked to write the expression using a single power of 10 (MP8). Students will extend this exponent rule to cases where the exponents are zero or negative in following lessons, but the focus here is on cases with positive exponents.
- Generalize a process for finding a power raised to a power, and justify (orally and in writing) that $(10^n)^m = 10^{n \boldcdot m}$.
Let's look at powers of powers of 10.
Required Preparation
Create a visual display (or add to an existing display) of the exponent rule to be displayed for all to see throughout the unit. A sample display can be seen in the Activity Synthesis.