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# 9.1: Exponent Rules

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Algebra I, Chapter 8, Lesson 2.

ID: 9730

Time required: 30 minutes

Topic: Polynomials

• Use technology to verify for various values of a and n\begin{align*}n\end{align*} that an=1an\begin{align*}a^{-n}=\frac{1}{a^n}\end{align*} where n\begin{align*}n\end{align*} is an integer.
• Evaluate simple numerical expressions raised to integral exponents (including zero exponents).
• Use technology to evaluate more complex numerical expressions involving exponents.

## Activity Overview

This activity allows students to work independently to discover rules for working with exponents, such as the Power of a Power rule. Students also investigate the value of a power whose exponent is zero or negative. As an optional extension, students investigate the value of a power whose exponent is a fraction with a numerator of one.

Teacher Preparation

• This activity is designed to be used in an Algebra 1 classroom. It can also be used in a Pre-Algebra classroom, or by any student learning the rules for operating with exponents.
• Students should already be familiar with basic powers, exponents, and bases, such as 23=8\begin{align*}2^3 = 8\end{align*}.
• While students can use the Calculator application at any time, you may wish to review the positive powers of two before beginning this activity (2, 4, 8, 16, 32, 64)\begin{align*}(2, \ 4, \ 8, \ 16, \ 32, \ 64 \ldots )\end{align*}.

Classroom Management

• This activity is intended to be mainly student-led, with breaks for the teacher to introduce concepts or bring the class together for a group discussion. Each student should have their own graphing calculator to work with.
• Information for an optional extension is provided at the end of this activity. Should you not wish students to complete the extension, you may have students disregard that portion of the worksheet.

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