This document discusses the distributive property and properties of exponents. It begins by defining the distributive property as a(b + c) = ab + ac and provides examples of using it. It then defines exponential form, where x is the base and y is the exponent. It presents properties of exponents, such as (am)(an) = am+n and (ab)m = ambm. It provides examples of simplifying expressions using these properties and evaluates expressions given specific values for variables.

1. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
Chapter 1.7
Distributive Property and
Properties of Exponents
Distributive Property
a ( b + c ) = ab + bc
1

2. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
Example
6( x + 2 )
6x + 6(2)
6x +12
Example
16 (15) ­ 16 (5)
2

3. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
Example
28 (10 1 )
7
1
28 (10 + 7 )
1
28 (10 ) + 28 ( 7 )
Exponential Form
y
x x is the BASE
y is the EXPONENT
3

4. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
4
(3) = (3)(3)(3)(3)
Look for a pattern
(­2)2(­2)3 = [(­2)(­2)][(­2)(­2)(­2)]
5
(­2)
Properties of Exponents
(am)(an) = a m + n (32)(34) = 36
(am)n = amn 3 2
(2 ) = 2 6
(ab)m = ambm (2)(3)2 = (22)(32)
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5. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
Properties of Exponents
__
a m 26
__ 2
= a m ­ n 4 = 2
an 2
a ( m am
__ 2 ( 2 22
__
(b = m
b (3 = 2
3
Simplify
( 4 . 3 )5
2
5

6. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
Simplify
2 3 4
(a b c)
Evaluate the expression
if a = 2 and b = ­3
2
(­2ab)
6

7. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
Evaluate the expression
if a = 2 and b = ­3
2
(2 ­ b)
Simplify
2 ( 4 + a ­ 3 )
7

8. Ch1.7_DistributiveAndExponentProperties.notebook August 30, 2011
Page 36
2 ­ 44 evens
8