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You are reading an older version of this FlexBook® textbook: Texas Instruments Algebra I Student Edition Go to the latest version.

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^x2^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{\;\;\;\;\;\;\;\;\;\;}

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Feb 22, 2012

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Apr 29, 2014
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