Exponent Rules

Exponent Rules
Math I – IV
Period 8 is great
Parts

When a number, variable, or expression is
raised to a power, the number, variable, or
expression is called the base and the power is
called the exponent.
b
n
What is an Exponent?


An exponent means that you multiply the base
by itself that many times.
For example
x4 =
x●x ●x●x
26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 = 64
The Invisible Exponent

When an expression does not have a visible
exponent its exponent is understood to be 1.
xx
1
Exponent Rule #1

When multiplying two expressions with the
same base you add their exponents.
b b b
n

m
nm
For example
2 4
 x
x x  x
2
1
2
1 2
3
22  2 2  2  2  8
2
4
6
Exponent Rule #1
b b b
n

m
nm
Try it on your own:
1. h  h  h
3
7
3 7
2 1
h
10
2. 3  3  3  3
 3  3  3  27
2
3
Exponent Rule #2

When dividing two expressions with the same
base you subtract their exponents.
b
b

n
m

b
nm
For example
x
4
x
2
 x
4 2
 x
2
Exponent Rule #2
n
b
nm

b
m
b

Try it on your own:
3.
h
6
h
2
 h
6 2
 h
4
3
4.
3
3
31
 3
3  9
2
Exponent Rule #3

When raising a power to a power you
multiply the exponents
(b )  b
n

m
nm
For example
(x )  x
2 4
2
2
(2 )  2
24
2 2
x
8
 2  16
4
Exponent Rule #3
(b )  b
n

m
nm
Try it on your own
3 2
5. (h )  h
2 2
6. (3 )  3
32
22
h
6
 3  81
4
Note

When using this rule the exponent can not be
brought in the parenthesis if there is addition
or subtraction
(x  2 )  x  2
2
2 2
4
You would have to use FOIL in these cases
4
Exponent Rule #4

When a product is raised to a power, each
piece is raised to the power
m
( ab)  a b

m
m
For example
2
(xy)  x y
2
2
( 2  5)  2  5  4  25  100
2
2
2
Exponent Rule #4
m
( ab)  a b

m
m
Try it on your own
3
7. ( hk )  h k
3
3
8. (2  3)  2  3  4  9  36
2
2
2
Note

This rule is for products only. When using this
rule the exponent can not be brought in the
parenthesis if there is addition or subtraction
( x  2)
2
 x 2
2
You would have to use FOIL in these cases
2
Exponent Rule #5

When a quotient is raised to a power, both the
numerator and denominator are raised to the
m
power
m
a
a
   m
b
b

For example
3
x
  
 y
x
3
y
3
Exponent Rule #5
m
m
a
a
   m
b
b

Try it on your own
2
2
h
h
9.    2
k
k
2
2
4
16
4
4
10.    2 
2
4
2
Zero Exponent

When anything, except 0, is raised to the zero
power it is 1.
a 1
0

( if a ≠ 0)
For example
x 1
0
25  1
0
( if x ≠ 0)
Zero Exponent
a 1
0

( if a ≠ 0)
Try it on your own
11. h  1
0
12. 1000  1
0
13. 0  0
0
( if h ≠ 0)
Negative Exponents


If b ≠ 0, then
b
n
For example
x
3
2
2



1
b
n
1
2
x
1
3
2

1
9
Negative Exponents


If b ≠ 0, then
n
b

Try it on your own:
14. h
15. 2
3
3


1
b
1
n
3
h
1
2
3

1
8
Negative Exponents

The negative exponent basically flips the part
with the negative exponent to the other half of
the fraction.
 1  b 
2
 b
 2   

b   1 
2
 2   2x 
2
  2x
 2   

x   1 
2
Math Manners

For a problem to be completely
simplified there should not be any
negative exponents
Mixed Practice
1.
6d
5
3d
9
4
 2d
59
 2d
4

2
d
5
2. 2e 4e  8e
45
 8e
9
4
Mixed Practice
 
3. q
4 5
q
45
q
20
4. 2lp   2 l p  32l 5 p 5
5
5 5
5
Mixed Practice
8 4
2
4
x y
( x y)
8 2 4  2
6 2

5.

x
y
x y
2
2 2
( xy)
x y
3
6.
(x x )
x
8 2
5 2
9

(x )
x
9

x
16
x
9
x
16 9
x
7
Mixed Practice
6
4 2
3
2
5 6
7. ( m n ) ( m n p )
 m n m n p
12
8
1218
m
18
n
8 12
m n p
30
20
12
p
30
30
30
Mixed Practice
8.
( x  2 y)
6
( x  2 y)
4
 ( x  2 y)
64
 ( x  2 y)
 ( x  2 y )( x  2 y )
F O I L
2
2
 x  2 xy  2 xy  4 y
2
2
 x  4 xy  4 y
2
Mixed Practice
6
9.
a d
5
4
9
a d
a
64

d
a
2
d
4
59
a d
2
4

Download Report