1. copyright©amberpasillas2010

2. 1 1 = +1 1 -1 = -1 -1 -1 = +1 -1 -1 -1 = -1 Multiply Integers REVIEW Odd # of Negatives = Negative Even # of Negatives = Positive -1 -1 = +1 -1 -1 -1 -1 -1 = -1 -1 -1 -1 = +1

3. copyright©amberpasillas2010 2 2 Means… 2 2 = 4 2 1 Means… 2 = 2 2 0 Means… 1 What does 2 -1 Mean?

4. copyright©amberpasillas2010 What does 2 -1 Mean? You cannot leave an exponent negative because there is no way to express it’s meaning. You must make it positive !

5. 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.

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 Definition of Negative Exponent For any integer n, a -n is the reciprocal of a n

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

10. copyright©amberpasillas2010 Follow the Pattern! = 3 3 3 = 3 = 3 = 1 = = = Notice that anything to the zero power is always one !

11. copyright©amberpasillas2010 Follow the Pattern! 2 10 3 4 5 100 1,000 10,000 100,000 1010 1 10 1 10 = 0.1 10 -2 1 1 10 2 1 100 = 0.01 10 -3 1 10 3 1 1000 = 0.001

12. 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

13. 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

14. copyright©amberpasillas2010 Zero Exponent: Negative Exponent:

15. copyright©amberpasillas2010 Simplify.

16. copyright©amberpasillas2010 Simplify.

17. copyright©amberpasillas2010 Simplify.

18. copyright©amberpasillas2010 Identity PropertyWhy It Works 3 2 3 -2 9 9 = 1 Any number to the zero power is ALWAYS ONE. x 0 = 1

19. copyright©amberpasillas2010 Take Out Your Study Guide !!!

20. Powers of Ten 2 10 3 4 5 100 1,000 10,000 100,000 1010 1 10 1 10 = 0.1 # 4 10 -2 1 1 10 2 1 100 = 0.01 10 -3 1 10 3 1 1000 = 0.001

21. copyright©amberpasillas2010 Negative Exponents # 5 EXAMPLES: For any integer n, a -n is the reciprocal of a n A negative exponent is an inverse!

22. copyright©amberpasillas2010 Any number to the zero power is ALWAYS ONE. x 0 = 1 Ex: # 6