1. More Multiplication Properties of Exponents
Section 7-4

2. Goals Goal Rubric To raise a power to a power.
To raise a product to a power.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary
None

4. Raising a Power to a Power
To find a power of a power, you can use the meaning of exponents.
= am  am  …  am
n factors
= a  a … a  a  a … a  a  a … a = amn
m factors
n groups of m factors
Notice the relationship between the exponents in the original power and the exponent in the final power:

5. Property: Power to a Power

6. Simplifying Exponents

7. Example: Raising a Power to a Power
Simplify.
Use the Power of a Power Property.
Simplify.
Use the Power of a Power Property.
Zero multiplied by any number is zero 1
Any number raised to the zero power is 1.

8. Example: Raising a Power to a Power
Simplify. C.
Use the Power of a Power Property.
Simplify the exponent of the first term.
Since the powers have the same base, add the exponents.
Write with a positive exponent.

9. Your Turn: Simplify. Use the Power of a Power Property. Simplify.
Zero multiplied by any number is zero.
Any number raised to the zero power is 1. 1

10. Your Turn: Simplify. Use the Power of a Power Property. c.
Simplify the exponents of the two terms.
Since the powers have the same base, add the exponents.

11. Raising a Product to a Power
Powers of products can be found by using the meaning of an exponent.

12. Example: Powers of Products
Simplify. A.
Use the Power of a Product Property.
Simplify. B.
Use the Power of a Product Property.
Simplify.

13. Example: Powers of Products
Simplify. C.
Use the Power of a Product Property.
Use the Power of a Product Property.
Simplify.

14. Your Turn: Simplify. Use the Power of a Product Property. Simplify.

15. Your Turn: Simplify. c. Use the Power of a Product Property.
Combine like terms.
Write with a positive exponent.

16. Joke Time What is the definition of a good farmer?
A man outstanding in his field!
What do you call a guy who never farts in public?
A private tutor!
What did the traffic light say to the car?
Don’t look, I’m changing!

17. Assignment
7-4 Exercises Pg : #10 – 50 even, 54 – 60 even