1. Exponents

2. 6³
Exponent
Base

3. 6³ is read “Six Cubed”
6³ = 6 x 6 x 6
6³ = 216

4. Any base to the zero power, equals one.
Example:
Any base to the first power, equals itself.
50 = 1
20 = 1
41 = 4
71 = 7

5. Evaluate Exponents Evaluating Exponents: means to find the VALUE of.
Example:
3² =
-9º =
(-3)³ =

6. Evaluate the following:
= =
= = 1
125 -9 3
100 64 1 16 -1 -7

7. Properties of Exponents
Complete the table in your notes and look for a pattern

8. Rule 1:
When multiplying two numbers with the same base, keep base and add the exponents.
3³ x 3² . x
3 x 3 x 3 x 3 x 3
3 x 3 x 3
3 x 3

9. Properties of Exponents
Complete the table in your notes and look for a pattern

10. Rule 2:
When dividing two numbers with the same base, keep base and subtract the exponents.

11. Rule 3 (3²) x (3²) x (3²) (3 x 3) x (3 x 3) x (3 x 3)
When raising a number with an exponent to a power, multiply the exponents.
(3²)³
(3²) x (3²) x (3²)
(3 x 3) x (3 x 3) x (3 x 3)
3 x 3 x 3 x 3 x 3 x 3

13. Negative Exponents Negative Exponents are NOT negative numbers
Negative Exponents are greater than 0, but less than one
Negative Exponents can be written as fractions and decimals

14. Using Positive Exponents
Expression
Using Positive Exponents
Value
102
100
101 10 1
10-1
1 .
0.1
10-2
0.01
10-3
103
0.001

15. Example
= = =

16. Simplify