Ch 8: ExponentsA) Product & Power Properties
Objective:
To recognize the properties of exponents anduse them to simplify expressions.
x
3
x x x
=
exponent
base
Base
The foundation of an expression that is raised toa power is known as the base.
Exponent
An exponent represents the number of times anexpression is multiplied by itself and is writtenin superscript.
Definitions
n n
n n n
x
a
=
x
b
x
a + b
n
3
=
n
2
n
3 + 2
Example:
=
n
5
n
5
1)Expand the bases as many times as the exponents states.
2)Count the number of times the variable appears – that isthe exponent.
Shortcut:
Evaluate the bases separately and ADD the exponents.
Product Property Rules
Example 1
Example 2
Example 3
Example 4
xx
x2 x3
xxx
=
x5
2xx
2x2 3x3
3xxx
=
6x5
2x2x
(2x)2 3x3
3xxx
=
12x5
2xyy
2xy2 −3x3y
3xxxy
=
−6x4y3
223
xxxxx
12
x5
2−3
xxxx
−6
x4
yyy
y3
Classwork
1)
2)
3)
4)
5)
6)
2 xxx 4 xxxxx = 8x8
-3 nnnnnnn 2nn = -6n9
-3 aaaa -2aa = 6a6
Example:
1)Expand the base (whatever is inside the parenthesis) as manytimes as the exponent states.
2)Continue expanding until there are no more exponents.
3)Count the number of times the variable appears – that isthe exponent.
Shortcut:
MULTIPLY the exponents.
( )
x
a
=
b
x
ab
( )
n
3
(n ) (n )
3
=
n
32
nnn nnn
=
n
6
2
3
Power to Power Property Rules
Example 5
Example 6
Example 7
Example 8
xx
(x2)3
xx
=
x6
2xx
(2x2)3
2xx
=
8x6
xx
2xx
222
xxxxxx
-2xx
(-2x2)3
-2xx
=
-8x6
-2xx
-2-2-2
xxxxxx
2xxy
(2x2y)3
2xxy
=
8x6y3
2xxy
222
xxxxxx
yyy
Classwork
1)
3)
2)
4)
5)
6)
