1. Multiplication of Exponents Notes

2. What is an Exponent? x4 = x ● x ● x ● x 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2
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

3. Vocabulary
Power – a number produced by raising a base to an exponent. (the term 27 is called a power.)
Exponential form – a number written with a base and an exponent. (23)
Exponent – the number that indicates how many times the base is used as a factor. (27)
Base – when a number is being raised to a power, the number being used as a factor. (27)

4. Parts of a Power
power 2 4
exponent
base
Say: “2 to the fourth power”

5. The Invisible Exponent
When an expression does not have a visible exponent its exponent is understood to be 1.

6. Zero Exponent
When anything, except 0, is raised to the zero power it is 1.
For example
( if a ≠ 0)
( if x ≠ 0)

7. Multiplication Rule
When multiplying two expressions with the same base you add their exponents.
For example

8. Example 1
(222)
(22222) 

9. Example 2
Written in multiplication form:
Using Rule:

10. Example 3

11. Example 4
Remember:

12. (-2x3y5)(3xy3)(x2y) -6x(3+1+2)y(5+3+1) -6x6y9 Example 5
Multiply coefficients and add exponents of like bases
-6x(3+1+2)y(5+3+1)
-6x6y9

13. Example 6 In order to simplify you must distribute first.
Since you are multiplying when you distribute you must use the multiplication rule for exponents.

14. You Try Simplify each expression1. 2. 3, 4. 5. 6.

15. You Try: Simplify (remember when adding only add coefficients of like terms)1. 2. 3. 4.