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.
Use your calculator to evaluate each of the expressions shown.
Then make a conjecture for .