Lesson 6: Rational Exponents

Module 2: Roots and Powers

 

Launch

This section checks to see if you have the prerequisite knowledge and skills to be able to complete this lesson successfully. 

Are you Ready?

Complete these questions in your course folder (binder). If you are experiencing difficulty, you may want to use the information and the multimedia in the Refresher section to clarify concepts before completing these exercises.

1. a.Outline the steps used to add/subtract fractions.
b. Outline the steps used to multiply fractions.
2. Evaluate the expressions without a calculator. Simplify where possible.

3. What is the formula relating a sphere’s volume and radius?
4. Find the radius of a sphere, to the nearest mm, if its volume is 905 mm³.
5. Name the parts of a power and the parts of a radical.

6. Simplify the following expressions. Report answers with positive exponents.

Once you have completed these exercises to the best of your ability, use the provided answer link to check your work.

Answers

If you feel comfortable with the concepts covered in the questions, move forward to Discover. If you experienced difficulties or want more practice, use the resources in Refresher to review these important concepts before continuing through the lesson or contact your teacher.

Refresher

Go to “Adding and Subtracting Fractions” to see how to add and subtract common fractions and improper fractions. The concepts of equivalent fractions and lowest common denominator are explained. This lesson also includes math problems and a math game.

Now watch “Multiplying Fractions.”

Materials

You will need the following to complete Math Lab: Powers and Radicals.

• scientific calculator

You worked with volumes of spheres and other 3-D objects in Module 1. While the aim of this lesson is not to revisit volume in particular, you will be working with cube roots and other radicals.

Read

Go to the textbook to review an example of how to find the radius of a sphere when you are given the volume.

In the last lesson you created a chart reviewing the exponent laws. You also added other laws you recently learned. Compare your chart to this one and be sure it is complete. Add one or two examples showing how the law is applied for each of the exponent laws.

Exponent Law	General Case
Product Law
Quotient Law
Power of a Power
Power of a Product
Power of a Quotient
Zero Exponent Law
Integral Exponent Law

 

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