Download 1. Exponent Properties

Section 6.1
Exponent Properties
Product of Powers Property
a a  a
m
n
m n
If you are multiplying two
terms with the same base, you
add the exponents.
2 2
4
6
 (2  2  2  2)( 2  2  2  2  2  2)
2
 1024
10
You try One!
3
5
9
x x x
x
3 5  9
x
17
Power of a Power Property
(a )  a
m n
mn
If you have a term raised to a
power that is raised to another
power, you multiply the
exponents.
2 
4 3
 (2  2  2  2)(2  2  2  2)(2  2  2  2)
43
2
12
2
 4096
You try One!
x 
9
3
x
27
You try One!
x 
7 2
72
x
14
x
Power of a Product Property
(ab)  a b
m
m m
If you have the product of
terms that is raised to a power,
you raise each term to that
power.
c3x h
3
2
c hc hc h
b gc
h
c hc h6
 3x 3x 3x
2
2
2
 3 3 3 x  x  x
3
6
 3 x
2
2
 27 x
2
You try One!
3xy 
6
2
3 x y
6
6
12
 729 x y
6
12
You try One!
2x 
4
2 x
4
 16x
4
4
Zero Exponent Property
a 1
0
Anything to the zero power is 1.
2
(19 x y )
1
0
You try One!
135x

0
91 29
y
1
Negative Exponent Property
a
m
1
 m
a
or
1
m

a
m
a
If a term is raised to a negative
exponent, you take the reciprocal
of that term.
1
2 
x x2
4
y
2 4 
x y x2
5
3x
3y

5
3
x
y
3
You try One!
4
3
1 1

3
4 64
You try One!
4x
3
4
 3
x
Quotient of Powers Property
m
a
mn

a
n
a
If you are dividing two terms
with the same base, you
subtract the exponents.
222222
2

3
2
222
6
2
6 3
2
8
3
You try One!
8
x
4
x
8 4
x
4
x
Which has more x’s the top or the bottom?
How many more?
You try One!
4
5
3x y
7 3
x y
2
3y
 3
x
Power of Quotients Property
m
a  a
 
m
b
b
m
If you have the quotient of
terms that are raised to a
power, you raise each term to
that power.
3
x 
 
 y 
2
6
x
3
y
You try One!
3
 4
 
 x
3
64
4

3
3
x
x
Scientific Notation
• Expand the following expressions.
2.13 10
5
 213000
2.47  10
5
 0.0000247
Try to Put a Few Together
x x
35 2

x
2
x
3
5
x
6
Try to Put a Few Together
1
3x 4
1 ( 2 )
4

x

3
x

x
2
x
 3x  x  3x
3
4
7
Try to Put a Few Together
3
5
3
5
14 x y
14 x y

2
6
2 6
2 x y
2x y
7x

y
Try to Put a Few Together
4
6x
2 3
2x y
2
3x
 3
y
Try to Put a Few Together
2 x 
2
3
2
x y
4
2
6
2 x
 2 4
x y
4
4x
 4
y
Try to Put a Few Together
5x y   3x
3
2 4
2
y
2
4
 625 x y  3x y
12
8
 1875 x y
10 12
4
Try to Put a Few Together
2
 3 x y  x y   3x   xy



 2y  2
2
2


2
xy
2
xy


3
4
2
3
5
2
5
9 x xy
9x y
 2

2
4y
2
8y
3
2
3
5
9x y

8
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From Textbook
6.1 #32 – 46 Even