Learning Resources
Lesson
This Focus is an application of the laws of exponents with zero, negative and rational exponents. Recall, these laws and click here for a simple review of these five laws if you have forgotten them.
Working with a partner, study the examples on p.167 - 168. For each step in the given examples you should be able to justify it with one of laws of exponents or the zero, negative and rational exponent definitions.
If you require further examples before beginning the Activities Section, go to the next page. Seek help from your teacher or classmates as your progress through the exercises since it is very important that you are able to use and apply exponents to their full capabilities.
For each example, use the interactive window to see each step of the solution.
Example 1
Simplify : 
Solution
Example 2
Prove that 
Solution
In this problem, the right side is as simple as can be expressed. Therefore, take the left side and simplify it to be the same as the right side.
Note that if the left side does not simplify to be the same as the right side in some problems, then you will have to simplify the right side as well to determine if they are the same.
Example 3
Evaluate 
Solution
Step through the interactive window one slide at a time to ensure that you understand the reason for each step.
Example 4
Solve for x: 
Solution
Sometimes we use the exponent laws in reverse. Note the use in the solution to this equation.
Go to the Activities Section and complete all exercises the more practice you get with these exponents the more skilled you will become working with them.
Activity
Check Your Understanding p.169 - 171. Complete 22 to 36 inclusive
Think About p. 171
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
- Simplify:
- Solve for x
- Evaluate:
Click here for suggested solutions.