Download 9.1 Simplifying Exponents

Warm-up
Given the function f(x)= -2x + 5, Evaluate :
1. f(2)
2. f(-3)
4. Simplify :
2
2
3x - 6x + 4x + 2x
 1
3. f  
2
Exponent
Rules
Exponents
The exponent of a number
says how many times to use
the number in a
multiplication.
2
8  8 8  64
8
2
Base
Exponent
Power of 1
Any number or variable
raised to the 1st power is itself.
Algebra:
Example:
1
a a
1
5 5
Power of 0
Any number or variable
raised to the zero power is 1.
Algebra:
Example:
0
a 1
0
5 1
Negative Exponent
Any number or variable raised to a
negative exponent becomes the
reciprocal.

1
Algebra:
1
a 
a
1

1
Example: 5

5
Multiplying
Powers with the Same Base
Add the exponents
Algebra:
Example:
m
n
m n
a a a
2
3
x x 
Raising a Power to
a Power
Multiply the exponents
Algebra:
a 
Example:
x 
m
7
n
3
mn
a

Dividing
Powers with Same Base
Subtract the exponents
m
a
m n
Algebra:

a
n
a
6
Example: x

4
x
Distribution
Distribute the exponent to
everything in the parentheses
Algebra:
Example:
 ab
m
 2x 
3
4
m
m
a b

TRY IT:
1.
2.
1
x 
 3 
x 
5
x 
 3
x 
5
4

2
3. 2x  3x
3
2
4
12x y
4.
2 2
3x y
3
5
2
5. 5x y  3x y
2
Exponents
Worksheet