1. Negative and Zero Exponents
Objectives:
Understand the concepts of negative and zero exponents
Simplify expressions containing negative and zero exponents

2. WHY???
Negative exponents allow you to apply the ideas that you have learned to more real-world situations. They are also useful for representing small quantities.

3. Definition of Negative Exponents
For all real numbers x and all integers n:

4. Negative Exponents
A negative exponent means you move the base to the other side of the fraction and make the exponent positive.
Notice that the base with the negative exponent moved and became positive!

5. You can’t leave the negative exponent!
Simplify.
You can’t leave the negative exponent!
The Secret
Where ever the largest positive exponent is located in the problem is where the exponent will be in the answer.

6. Examples Evaluate the following expressions.
Rewrite the following expressions using positive exponents.
Solutions

7. Examples:
Evaluate each expression.

8. Evaluate the following. . .

9. Zero as an Exponent
For any nonzero number x,

10. Zero Exponents Anything to the 0 power is equal to 1. a0 = 1
True or False? Anything divided by itself equals one.
True!
See for yourself!

11. Simplify.
x-4 y0 You can not have negative or zero exponents in your answer.

12. Examples
Evaluate the following expressions.
Solutions

13. You Try It Evaluate the following expressions.
Rewrite the following expressions with positive exponents.

14. Problem 1

15. Problem 2