Download 6.1 Using Properties of Exponents

6.1 Using
Properties of
Exponents
p. 323
Properties of Exponents
a&b are real numbers, m&n are integers
•
Product Property: am * an=am+n
•
Power of a Power Property: (am)n=amn
•
Power of a Product Property: (ab)m=ambm
1
a-m= a m
•
Negative Exponent Property:
•
•
Zero Exponent Property: a0=1; a≠0
Quotient of Powers: am = am-n; a≠0
an
Power of Quotient:  a  m a m b≠0
•
   m
b
b
; a≠0
Example 1 – Product Property
•
*
=
• (-5)4+5 =
9
• (-5) =
• -1953125
4
(-5)
5
(-5)
Example 2
•
* =
5+2
• x =
7
• x
5
x
2
x
Example 3 – Power of a Power
•
=
3*4
• 2 =
12
• 2 =
• 4096
3
4
(2 )
Example 4
•
=
4*2
• 3 =
8
• 3 =
• 6561
4
2
(3 )
Example 5 – Neg. Exponent
•
=
• (-5)-6+4 =
-2
• (-5) =
-6
4
(-5) (-5)
1
1

2
 5 25
Example 6 – Quotient of
Powers
5
x

3
x
x
5 3
 x
2
Example 7 – Power of
Quotient
2
 r 
r
 5   5 2 
s 
s 
2
2
r

10
s
2 10
r s
Example 8 – Zero Exponent
•
=
• 72 b-3*2 b5 b =
• 49 b-6+5+1 =
• 49b0 =
• 49
-3
2
5
(7b ) b b
Example 9 – Quotient of
Powers
5
x

10
x
x
5 10
x
5
1
 5
x
Scientific Notation
• 131,400,000,000=
1.314 x 1011
Put that number here!
Move the decimal
behind the 1st number
How many
places did you
have to move
the decimal?
Example – Scientific Notation
• 131,400,000,000 =
•
5,284,000
1.314 x 1011 =
5.284 x 106
1.314
5
11 6
*10
 .249 *10  24,900
5.284
Assignment