1. Negative Exponents
Chapter 4
Section 4.6

2. Objective
Students will solve problems involving negative exponents

3. Concept
You have learned the meaning of an when n is a positive number. For example: 23 = 8 22 = 4 21 = 2

4. Concept
In this lesson you will consider the meaning of expressions like 20 and 2-1 that have zero and negative integers as exponents.

5. Definition of a-n
If a is a nonzero real number and n is a positive integer, a-n = 1/an

6. Example

7. concept
m > n am/an = am-n = a7/a3 = a7-3 = a4 m < n am/an = 1/an-m = a3/a7 = 1/a7-3 = 1/a4 m = n am/an = am-n = a0 = a5/a5 = a5-5 = a0 = 1

8. If a is a nonzero real number a0 = 1 The expression 00 has no meaning
Definition of a0
If a is a nonzero real number a0 = 1 The expression 00 has no meaning

9. Concept
a5 = a5-5 = a0 a5 But you already know that a5 = 1 This is what leads us to the previous definition (a0)

10. concept Multiplying like bases, add exponents
Dividing like bases, subtract exponents
Numbers raised to exponents, goes to all numbers
Power to a Power, multiply exponents

11. Example
Simplify. Give your answers using positive exponents 5/5-3 (b-1)-3 (3x-1)2

12. Questions

13. Assignment
Worksheet