1. copyright©amberpasillas2010

2. What does 2 -1 Mean? You cannot leave an exponent negative because there is no way to express it’s meaning.

3. 2 * 2 2 * 2 * 2 What happens when you have a negative exponent? 2 -1 = ? Well to find out what 2 the negative 1 is. Let’s look at: 1 1 1 1 1212 = Therefore, 2 -1 =

4. copyright©amberpasillas2010 You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals. If the negative exponent is on top, move it to the bottom.

5. copyright©amberpasillas2010 Definition of Negative Exponent For any integer n, a -n is the reciprocal of a n

6. copyright©amberpasillas2010 Definition of Negative Exponent For any integer n, a -n is the reciprocal of a n

7. copyright©amberpasillas2010 Definition of Negative Exponent For any integer n, a -n is the reciprocal of a n

8. copyright©amberpasillas2010 Simplify. A negative exponent is an inverse! Flip the number over to make the exponent positive!

9. 2 * 2 * 2 What happens when you have an exponent of zero? 2 0 = ? Well to find out what 2 the zero power is. Let’s look at: 1 1 1 1 1 1 1111 = 1= Therefore, 2 0 = 1

10. Any number to the zero power, except zero is equal to 1. 6 0 = 1 10 0 = 1 19 0 = 1 Zero to the zero power is undefined, meaning that it does not exist.

11. copyright©amberpasillas2010 Study the table and FOLLOW THE PATTERN! Exponent, n 2 5 2 4 2 3 2 2 2 1 2 0 2 –1 2 –2 2 –3 Power, 2 n 32168421 1212 1414 1 8 What do you think 2 –4 will be? 2 –4 = 1 = 1 2 4 16 What do you think 2 –5 will be? 2 –5 = 1 = 1 2 5 32

12. copyright©amberpasillas2010 Study the table and FOLLOW THE PATTERN! Exponent, n 3 5 3 4 3 3 3 2 3 1 3 0 3 –1 3 –2 3 –3 Power, 3 n 2438127931 1313 1919 1 27 What do you think 3 –4 will be? 3 –4 = 1 = 1 3 4 81 What do you think 3 –5 will be? 3 –5 = 1 = 1 3 5 243

13. copyright©amberpasillas2010 Zero Exponent: Negative Exponent:

14. copyright©amberpasillas2010 Simplify.

15. copyright©amberpasillas2010 Simplify.

16. copyright©amberpasillas2010 Simplify.

17. copyright©amberpasillas2010 Power to Power Rule ( ) x a = b x ab ( ) 2 3 = -2 2 3(-2) = 2 -6 = = ( ) 8 -2 = = Negative exponents follow rules of exponents.

18. copyright©amberpasillas2010 Simplify in two different ways. When dividing fractions, multiply the first fraction by the reciprocal of the second fraction.

19. copyright©amberpasillas2010 Simplify in two different ways.