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

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.


• 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


(a6)3

Lesson Practice


(52)2

Lesson Practice


(b4)7


• 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


(7a3b5)3

Lesson Practice


(2a2b4)2

Example 4Simplifying a Power of a Product


(–2y4)3

Lesson Practice


(–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?


Example 6Simplifying a Power of a Quotient


Example 7Simplifying a Power of a Quotient


Lesson Practice


Lesson Practice



• 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


(4xy2)2 (2x3y)2

Example 9Simplifying Expressions with Powers


(– 5x–2 )2 (3xy2)4

Lesson Practice


(9ab–2 )2 (2a2b4)

Documents

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