9.1: Exponent Rules
This activity is intended to supplement Algebra I, Chapter 8, Lesson 2.
In this activity, you will explore:
- expressions involving products and quotients with exponents
- expressions with negative and zero exponents
Before beginning the activity, clear out all functions from the screen and turn off all stat plots.
Problem 1 - Discovering Exponent Rules
Run the ExpRules program by pressing PRGM then choosing it from the menu and pressing ENTER.
This program allows you to explore 6 different rules of exponents by helping you evaluate exponential expressions for different values of and . To begin, choose Experiment, then type 1 to explore Rule 1.
The program displays the expression that you will be calculating to explore Rule 1, . Calculate the expression several times, choosing values from 1 through 8 for and . Make and test a conjecture.
Repeat this process to explore rules . Pay attention to the prompts, as some rules require you to enter negative values for the variables. Record your conjectures below.
- Rule 1: Make a rule for the product of two powers with like bases.
- Rule 2: Make a rule for the quotient of two powers with like bases.
- Rule 3: Make a rule for the power of a power.
- Rule 4: Make a rule for a power with a negative exponent.
- Rule 5: Make a rule for a power with a zero exponent.
- Rule 6: Make a rule for the power of a quotient.
Extension
Use your calculator to evaluate each of the expressions shown.
Then make a conjecture for .
Complete: