1. Properties of Rational Exponents
Section 7.2

2. Agenda Math Talk Expectations
Come up with what happens when students do not follow expectations
Number Talk
Review Last weeks test
5. Start rational exponents!

3. Number Talk
Devonte received $ 500 which was 115% of a number. He has to give 75% of that number to Larry. How much will Larry receive?

4. What You Will Learn: 1. Simplify expressions with rational exponents.
2. Use properties of rational exponents.
3. Write an expression involving rational exponents in simplest form.
4. Perform operations with rational exponents.
5. Simplify expressions that have variables and rational exponents.
6. Write an expression involving variables and rational exponents in simplest form.
7. Perform operations with rational exponents and variables.

5. Properties of Rational Exponents
Property: Example: 1.
2. (am)n = amn
3. (ab)m = ambm 4.

6. Properties of Rational Exponents (cont.)
Property: Example: 5. 6.

7. Using the Properties
Simplify the expressions: 1. 2. 3.

8. More Fun with Properties4. 5.

9. You Try
Simplify: 1. 2. 3. 4. 5.

10. More Simplifying
Simplify the expressions: 1. 2.

11. You Try
Simplify: 1. 2.

12. Simplest Form - continued
In order for a radical to be in simplest form, you have to remove any perfect nth powers and rationalize denominators. Example:
Write in simplest form:

13. Write in simplest form: 1.
You Try
Write in simplest form: 1. 2.

14. Operations Using Radicals
Two radicals expressions are “like radicals” if they have the same index and the same radicand. Example:
Perform the indicated operation:

15. You Try
Perform the indicated operation: 1. 2.

16. Simplifying Expressions Involving Variables
Important!
= x when n is odd.
= |x| when n is even.

17. Simplifying
Simplify the expression. Assume all variables are positive:

18. Simplify the expression. Assume all variables are positive. 1. 2. 3.
You Try
Simplify the expression. Assume all variables are positive. 1. 2. 3. 4.

19. Writing Variable Expressions in Simplest Form
Write the expression in simplest form. Assume all variables are positive.

20. You Try
Write the expression in simplest form. Assume all variables are positive. 1. 2.

21. Adding and Subtracting Expressions Involving Variables
Perform the indicated operation. Assume all variables are positive. 3.

22. You Try
Perform the indicated operations. Assume all variables are positive. 1. 2. 3.