1. Bell Quiz

2. Objectives Learn to simplify expressions by using three new properties for exponents: – The Power of a Power Property – The Power of a Product Property – The Power of a Quotient Property

3. Properties for Exponents Previous lessons have explored expressions involving exponents. Several rules and definitions have been developed.

4. Properties for Exponents There is another property of exponents that involves raising a power to a power.

5. Example 1 Simplifying a Power of a Power Simplify the expression. (2 3 ) 2

6. Example 2 Simplifying a Power of a Power Simplify the expression. (a 6 ) 3

7. Lesson Practice Simplify the expression. (5 2 ) 2

8. Lesson Practice Simplify the expression. (b 4 ) 7

9. Properties for Exponents The Power Property and the Product Property of Exponents can be used together to formulate a rule for the power of a product.

10. Example 3 Simplifying a Power of a Product Simplify the expression. (7a 3 b 5 ) 3

11. Lesson Practice Simplify the expression. (2a 2 b 4 ) 2

12. Example 4 Simplifying a Power of a Product Simplify the expression. (–2y 4 ) 3

13. Lesson Practice Simplify the expression. (–3n 4 ) 2

14. Example 5 Application: Interior Design A square family room is being measured for carpeting. If the length of one side of the room is 2x feet, what is the area of the room?

15. Lesson Practice A shipping container is in the shape of a cube with a side length of 3x inches. What is the volume of the container?

16. Properties for Exponents

17. Example 6 Simplifying a Power of a Quotient Simplify the expression.

18. Example 7 Simplifying a Power of a Quotient Simplify the expression.

19. Lesson Practice Simplify the expression.

20. Lesson Practice Simplify the expression.

21. Properties for Exponents The rules for exponents apply to many expressions with powers. When simplifying expressions, be sure to follow the order of operations.

22. Example 8 Simplifying Expressions with Powers Simplify the expression. (4xy 2 ) 2 (2x 3 y) 2

23. Example 9 Simplifying Expressions with Powers Simplify the expression. (– 5x –2 ) 2 (3xy 2 ) 4

24. Lesson Practice Simplify the expression. (9ab –2 ) 2 (2a 2 b 4 )