More Multiplication Properties of Exponents Section 7-4

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.

Vocabulary None

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:

Property: Power to a Power

Simplifying Exponents

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.

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.

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

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.

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

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

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

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

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

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!

Assignment 7-4 Exercises Pg. 462 - 464: #10 – 50 even, 54 – 60 even