Transcript Chapter 6

Chapter 6
Section 1: Using Properties of
Exponents
Scientific Notation
A number is expressed in Scientific Notation if it is in
the form
c  10n or c X 10n or cEn
where 1 |c|  10 and n is an integer.
Example: The width of a molecule of water is about
2.5 X 10-8 meter
or
0.000000025 meter.
Choose all that apply. Which of the
following are in scientific notation?
5
10
A)3.1 x
B)12 x 105
C)6 x 10-2
D)0.12 x 10-2
E)-5 x 103.8
In 1997 Denmark had a population of 5,284,000 and a
gross domestic product (GDP) of $131, 400, 000,
000.
Write the population and GDP in scientific notation.
5,284,000
$131, 400, 000, 000
=5.284 x 106
=$1.314 x 1011
Write the following in scientific
notation
• 325
• 120 000
VOCABULARY
• Power - 23
• Base – 2
• Exponent - 3
23
Recall multiplying 2 powers with the
same base:
2325
(222)  (22222) = 28
5453
(5555)  (555) = 57
PROPERTIES OF
EXPONENTS
Let a and b be real numbers and let m and n be integers.
PROPERTY NAME
DEFINITION
EXAMPLE
Product of Powers
aman = am+n
535-1 = 53+(-1) = 52 = 25
Quotient of Powers
Power of a Power
(am)n = amn
Power of a Product
(ab)m
=
am  amn, a  0
an
65
5 2
3

6

6
 216
2
6
(33)2 = 332 = 36 = 729
a mb m
(continued)
(23)4 = 2434 = 1296
PROPERTIES OF
EXPONENTS
Let a and b be real numbers and let m and n be integers.
PROPERTY NAME
DEFINITION
EXAMPLE
Quotient of Powers
am  amn, a  0
an
5
6
5 2
3

6

6
 216
62
Negative Exponent**
Zero Exponent
a m 
1
,a  0
am
7 2  1  1
72 49
a0 = 1, a  0
(-89)0 = 1
Power of a Quotient




a 
b 
m
m
 am , b  0
b
2
 4 


 7 

42
72

16
49
EVALUATING NUMERICAL
EXPRESSIONS
(23)4
=(8)4
3


4


2
(-5)-6 (-5)4
 115

 118





(-6*35)3
2
 32

 42

=4096





9
16
=(-5)-6+4
 118

 115





2
=(-6*243)3

=(-5)-2

 113

2
1
( 5) 2

 116
=(-1458)3
3099363912
3.099363912 x 109
1
25
A swarm of locusts may contain as many as 85
million locusts per square kilometer and cover an
area of 1200 square kilometers.
Write the density of locusts in scientific
notation.
1 million =1 x 106
85 million
=8.5 x 107
=85 x 106
SIMPLIFYING ALGEBRAIC
EXPRESSION
(7b-3)2 b5b
xy 
2
2
x 3 y 1
w
3
x 2 w 6 x 1 
HW: 6.1#18-45x3