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Warm Up Write each expression using an exponent. 1. 2 • 2 • 2 2. x • x • x • x 3. Write each expression without using an exponent. 4. 4 3 5. y 2 6. m –4. Learning Targets. Use the Power of a Product Property. Use the Power of a Power Property. - PowerPoint PPT Presentation
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Holt Algebra 1
70 Multiplication Properties of Exponents
Warm Up
Write each expression using an exponent.1. 2 • 2 • 2
2. x • x • x • x
3.
Write each expression without using an exponent.
4. 43
5. y2
6. m–4
Holt Algebra 1
70 Multiplication Properties of Exponents
Use the Power of a Product Property
Learning Targets
Use the Power of a Power Property
Holt Algebra 1
70 Multiplication Properties of Exponents
Holt Algebra 1
70 Multiplication Properties of Exponents
Products of powers with the same base can be found by writing each power as a repeated multiplication.
Notice the relationship between the exponents in the factors and the exponents in the product 5 + 2 = 7.
Holt Algebra 1
70 Multiplication Properties of Exponents
Simplify.
Example 1: Finding Products of Powers
A.
Since the powers have the same base, keep the base and add the exponents.
B.
Group powers with the same base together.
Add the exponents of powers with the same base.
Holt Algebra 1
70 Multiplication Properties of Exponents
http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=6359/6359.xml
Holt Algebra 1
70 Multiplication Properties of Exponents
Simplify.
Example 1: Finding Products of Powers
C.
D.
1
Group powers with the same base together.
Add the exponents of powers with the same base.
Group the positive exponents and add since they have the same base
Add the like bases.
Holt Algebra 1
70 Multiplication Properties of Exponents
On Your Own Example 1
a. Simplify.
b.
c.
d.
Holt Algebra 1
70 Multiplication Properties of Exponents
To find a power of a power, you can use the meaning of exponents.
Notice the relationship between the exponents in the original power and the exponent in the final power:
Holt Algebra 1
70 Multiplication Properties of Exponents
Simplify.
Example 3: Finding Powers of Powers
Use the Power of a Power Property.
Simplify.
1
Use the Power of a Power Property.
Zero multiplied by any number is zero
Any number raised to the zero power is 1.
Holt Algebra 1
70 Multiplication Properties of Exponents
http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7725/7725.xml
Holt Algebra 1
70 Multiplication Properties of Exponents
Simplify.
Example 3: Finding Powers of Powers
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.
C.
Holt Algebra 1
70 Multiplication Properties of Exponents
On Your Own Example 3
Simplify.
c.
Holt Algebra 1
70 Multiplication Properties of Exponents
Example 4: Finding Powers of Products
Simplify.
Use the Power of a Product Property.
Simplify.
Use the Power of a Product Property.
Simplify.
A.
B.
Holt Algebra 1
70 Multiplication Properties of Exponents
http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7726/7726.xml
Holt Algebra 1
70 Multiplication Properties of Exponents
Example 4: Finding Powers of Products
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property.
Simplify.
C.
Holt Algebra 1
70 Multiplication Properties of Exponents
On Your Own Example 4
Simplify.c.
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