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# 9.1: Exponent Rules

Created by: CK-12

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 $Y=$ 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 $x$ and $y$. 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, $2^x$$2^y$. Calculate the expression several times, choosing values from 1 through 8 for $x$ and $y$. Make and test a conjecture.

Repeat this process to explore rules $2 - 6$. 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 $m^\frac{1}{n}$.

$36^\frac{1}{2} = \underline{\;\;\;\;\;\;\;} && 8^\frac{1}{3} = \underline{\;\;\;\;\;\;\;} && 49^\frac{1}{2} = \underline{\;\;\;\;\;\;\;} && 16^\frac{1}{2} = \underline{\;\;\;\;\;\;\;} && 16^\frac{1}{4} = \underline{\;\;\;\;\;\;\;}$

Complete: $m^\frac{1}{n} = \underline{\;\;\;\;\;\;\;\;\;\;}$

Feb 22, 2012

Oct 31, 2014