1. Exponents

2. 6³
Exponent
Base

3. (repeated multiplication)
6³ is read “Six Cubed”
6³ means 6 x 6 x 6
(repeated multiplication)
6³ = 216

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

5. Evaluate Exponents Evaluating Exponents: means to find the VALUE of.
Example:
3² =
-9º =
(-3)³ = 9 -1
-27

6. Tricky Integer Bases =
Exponents tell you how many times to multiply the base
Positive Base
Negative Base
Evaluate:
Evaluate: -9 9
** Now check your answer with your calculators **

7. (-3) -3 (-3) • (-3) 9 (-3) • (-3) • (-3) -27 (-3) • (-3) • (-3) • (-3)
Expression
Expanded Form
Evaluated Solution
Expression
Expanded Form
Evaluated Solution
(-3)
-3 
 (-3) • (-3)  9
 (-3) • (-3) • (-3)
 -27
 (-3) • (-3) • (-3) • (-3)
 81
What patterns do you notice?

8. If you have a negative base and an odd exponent , the answer is negative.
Example:
If you have a negative base and an even exponent , the answer is positive.
(-5)1 = -5
(-5)3 =
(-5)2 = 25
(-5)4 =

9. 1 1 3
125 1
625 -9
100 16 1 -1 -7 -1

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

11. 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

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

13. Rule 2:
When dividing two numbers with the same base, keep base and subtract the exponents.
Why does x0 = 1?

15. 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

17. Using Positive Exponents
Expression
Using Positive Exponents
Value
102
100
101 10 1
10-1
1 .
10-2
10-3
103
1000

18. 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

19. Negative Exponents Video
Example
= = = =
Negative Exponents Video

20. Simplify