7-1 MULTIPLICATION PROPERTIES OF EXPONENTS. EXAMPLE 1: SIMPLIFY.
Bell Quiz. Objectives Learn to simplify expressions by using three new properties for exponents: –...
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Transcript of Bell Quiz. Objectives Learn to simplify expressions by using three new properties for exponents: –...
![Page 1: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/1.jpg)
Bell Quiz
![Page 2: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/3.jpg)
Properties for Exponents
• Previous lessons have explored expressions involving exponents.
• Several rules and definitions have been developed.
![Page 4: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/4.jpg)
Properties for Exponents
• There is another property of exponents that involves raising a power to a power.
![Page 5: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/5.jpg)
Example 1Simplifying a Power of a Power
Simplify the expression.
(23)2
![Page 6: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/6.jpg)
Example 2Simplifying a Power of a Power
Simplify the expression.
(a6)3
![Page 7: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/7.jpg)
Lesson Practice
Simplify the expression.
(52)2
![Page 8: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/8.jpg)
Lesson Practice
Simplify the expression.
(b4)7
![Page 9: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/9.jpg)
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.
![Page 10: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/10.jpg)
Example 3Simplifying a Power of a Product
Simplify the expression.
(7a3b5)3
![Page 11: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/11.jpg)
Lesson Practice
Simplify the expression.
(2a2b4)2
![Page 12: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/12.jpg)
Example 4Simplifying a Power of a Product
Simplify the expression.
(–2y4)3
![Page 13: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/13.jpg)
Lesson Practice
Simplify the expression.
(–3n4)2
![Page 14: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/14.jpg)
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?
![Page 15: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/15.jpg)
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?
![Page 16: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/16.jpg)
Properties for Exponents
![Page 17: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/17.jpg)
Example 6Simplifying a Power of a Quotient
Simplify the expression.
![Page 18: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/18.jpg)
Example 7Simplifying a Power of a Quotient
Simplify the expression.
![Page 19: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/19.jpg)
Lesson Practice
Simplify the expression.
![Page 20: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/20.jpg)
Lesson Practice
Simplify the expression.
![Page 21: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/21.jpg)
Properties for Exponents
• The rules for exponents apply to many expressions with powers.
• When simplifying expressions, be sure to follow the order of operations.
![Page 22: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/22.jpg)
Example 8Simplifying Expressions with Powers
Simplify the expression.
(4xy2)2 (2x3y)2
![Page 23: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/23.jpg)
Example 9Simplifying Expressions with Powers
Simplify the expression.
(– 5x–2 )2 (3xy2)4
![Page 24: 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.](https://reader035.fdocuments.in/reader035/viewer/2022081521/5a4d1b0d7f8b9ab05998c4b3/html5/thumbnails/24.jpg)
Lesson Practice
Simplify the expression.
(9ab–2 )2 (2a2b4)