Transcript Exponent Rules - Chignecto-Central Regional School Board

Exponent Rules
Everybody Got Time For That!
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
nm
n
m
b b b

Try it on your own:
3 7
1. h  h  h  h
2
2 1
3
2. 3 3  3  3
 3  3  3  27
3
7
10
Exponent Rule #2

When dividing two expressions with the same
base you subtract their exponents.
n
b
n

m

b
m
b

For example
4
x
4 2
2

x x
2
x
Exponent Rule #2
n
b
nm

b
m
b

Try it on your own:
6
h
6 2
4
3. 2  h  h
h
3
3
31
2
4.
 3 3  9
3
Exponent Rule #3

When raising a power to a power you
multiply the exponents
(b )  b
n m

nm
For example
(x )  x  x
2 2
22
4
(2 )  2  2  16
2 4
24
8
Exponent Rule #3
(b )  b
n m

nm
Try it on your own
3 2
5. (h )  h
2 2
32
22
6. (3 )  3
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
4
You would have to use the Distributive Property in these cases
Exponent Rule #4

When a product is raised to a power, each
piece is raised to the power
(ab)  a b
m

m m
For example
(xy)  x y
2
2
2
(2  5)  2  5  4 25  100
2
2
2
Exponent Rule #4
(ab)  a b
m

m m
Try it on your own
7. (hk )  h k
3
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)  x  2
2
2
2
You would have to use the Distributive Property in these cases
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
x
   3
y
y
 
3
Exponent Rule #5
m
a
a
   m
b
b

m
Try it on your own
2
h
h
9.    2
k
k
2
2
4
16
4
4
10.    2 
2
4
2
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
0
( if a ≠ 0)
a 1

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

For example
b
n
2
x 
2
3 

1
n
b
1
2
x
1 1

2
3
9
Negative Exponents


1
b  n
b
Try it on your own:
1
3
14. h  3
h
1 1
3
15. 2  3 
2
8
If b ≠ 0, then
n
Negative Exponents

The negative exponent basically flips the part
with the negative exponent to the other half of
the fraction.
 1  b 
2
 2      b
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
5
6d
2
5 9
4
1.

2
d
 2d  4
9
3d
d
2. 2e 4e  8e
4
5
45
 8e
9
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
2
4
8
4
x y
( x y)
8 2 4  2
6 2

5.

x
y
x y
2
2 2
( xy)
x y
3 5 2
8 2
16
(x )
x
(x x )
169
7


6.

x
x
9
9
9
x
x
x
Mixed Practice
6 4 2
3 2
5 6
7. (m n ) (m n p )
12 8
18 12 30
 m n m n p
1218 812 30
m n p
30 20 30
m n p
Mixed Practice
( x  2 y)
6 4
2
8.
 ( x  2 y)
4  ( x  2 y)
( x  2 y)
6
 ( x  2 y)( x  2 y)
F O
I
L
 x  2 xy  2 xy  4y
2
2
 x  4 xy  4 y
2
2
Mixed Practice
6
5
ad
6  4 5 9
9. 4 9  a d  a 2 d 4
a d
2
a
 4
d