Transcript More Multiplication Properties of Exponents

More Multiplication Properties of
Exponents
Section 7-4
Goals
Goal
• To raise a power to a power.
• To raise a product to a
power.
Rubric
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
m factors
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.
Use the Power of a Power Property.
Zero multiplied by any number is zero.
1
Any number raised to the zero power
is 1.
Your Turn:
Simplify.
c.
Use the Power of a Power Property.
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.
Use the Power of a Product Property.
Use the Power of a Product Property.
Simplify.
Your Turn:
Simplify.
c.
Use the Power of a Product
Property.
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