Exponents
Objective: to evaluate expressions with
exponents.
Vocabulary:
Power: A number produced by rising a base to
an exponent.
Exponential Form: A number written with a
base and an exponent.
Ex: 3•3•3•3 = 3
Exponent: The number that indicates how many
times the base is used as a factor.
Base: The number being used as a factor
Evaluating powers
Ex 1) 4
= 4 · 4 · 4 = 64
Ex 2) ( - 8)
= (-8) · (-8) = 64
Ex 3) - 5 = -5 · 5 = -25
Ex 4) ( 2
- 3 ) + 6( 4) = 2 · 2 · 2 · 2 · 2 - 3 · 3 + 24 = 32
- 9 + 24 = 47
Objective: to apply the properties of
exponents to evaluate the zero exponent
Notice that 5 · 5 · 5 · 5 · 5 · 5 = 5
It can also be written as (5 · 5 · 5) · (5 · 5 ·
5) or 5 · 5 What other ways could we write this power?
To multiply powers with the same base, keep the base and add
the exponents.
Ex 1) 6 · 6 = 6
Ex 2) n · n
= n
Ex 3) 2 · 2 = 2
Ex 4) 5 · 3 can’t do
Notice that 
which can be reduced to 2
So to divide powers with the same base, keep the base the same
and subtract the exponents. 
The ZERO power:
| 2 |
2 · 2 · 2 · 2 |
16 |
|
| 2 |
2 · 2 · 2 |
8 |
16 ÷ 2 |
| 2 |
2 · 2 |
4 |
8 ÷ 2 |
| 2 |
2 |
2 |
4 ÷ 2 |
2 |
|
1 |
2 ÷ 2 |
The zero power of ANY number except zero is always 1.
