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Properties for Exponents Previous lessons have explored expressions involving exponents. Several rules and definitions have been developed.
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Bell Quiz
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
Properties for Exponents
• Previous lessons have explored expressions involving exponents.
• Several rules and definitions have been developed.
Properties for Exponents
• There is another property of exponents that involves raising a power to a power.
Example 1Simplifying a Power of a Power
Simplify the expression.
(23)2
Example 2Simplifying a Power of a Power
Simplify the expression.
(a6)3
Lesson Practice
Simplify the expression.
(52)2
Lesson Practice
Simplify the expression.
(b4)7
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.
Example 3Simplifying a Power of a Product
Simplify the expression.
(7a3b5)3
Lesson Practice
Simplify the expression.
(2a2b4)2
Example 4Simplifying a Power of a Product
Simplify the expression.
(–2y4)3
Lesson Practice
Simplify the expression.
(–3n4)2
Example 5Application: 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?
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?
Properties for Exponents
Example 6Simplifying a Power of a Quotient
Simplify the expression.
Example 7Simplifying a Power of a Quotient
Simplify the expression.
Lesson Practice
Simplify the expression.
Lesson Practice
Simplify the expression.
Properties for Exponents
• The rules for exponents apply to many expressions with powers.
• When simplifying expressions, be sure to follow the order of operations.
Example 8Simplifying Expressions with Powers
Simplify the expression.
(4xy2)2 (2x3y)2
Example 9Simplifying Expressions with Powers
Simplify the expression.
(– 5x–2 )2 (3xy2)4
Lesson Practice
Simplify the expression.
(9ab–2 )2 (2a2b4)
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