1. copyright©amberpasillas2010

2. For Learning to Happen: Remove all other thoughts from your mind. This lesson is a challenge so please follow along with what I am teaching you. Pay close attention to this lesson. Try all of the examples. Ignore all other distractions.

3. copyright©amberpasillas2010 An exponent is written in exponential form when it is simplified using exponents. 32a332a3 Exponential Form

4. copyright©amberpasillas2010 32a332a3 An exponent is written in factor form when it is written out. = 33aaa Factor Form

5. copyright©amberpasillas2010 = 2 2 2 2 2 2 4 8 16 5 32 How to Multiply Out Exponents

6. copyright©amberpasillas2010 When s implifying exponents y ou must watch the sign a nd the p arenthesis ! 5 2 = 5 5 = 25 –5 2 = – (5) ( 5) = –25 (-5) 2 = (-5) ( -5) = 25 –(5) 2 = - (5) ( 5) = –25 1 1

7. copyright©amberpasillas2010 Simplify.

8. copyright©amberpasillas2010 Here is why any number to the zero power is 1. Positive Exponents Repetitive Multiplication Identity Property: Any number multiplied by one equals itself.

9. copyright©amberpasillas2010 Here is why any number to the zero power is 1. Positive Exponents Repetitive Multiplication a0 a0 = 1 Notice there are zero “a’s” present. However, there is still a one because of the Identity Property.

10. 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. If the negative exponent is on bottom, move it to the top.

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

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13. Negative Exponents Repetitive Division A negative exponent is an inverse! Follow the pattern for Negative Exponents!

14. copyright©amberpasillas2010 Just flip the fraction over to make the exponent positive!

15. Just flip the fraction over to make the exponent positive!

16. copyright©amberpasillas2010 Just flip the fraction over to make the exponent positive!

17. copyright©amberpasillas2010 Just flip the fraction over to make the exponent positive!

18. copyright©amberpasillas2010 Rewrite s o there is NO negative exponent. HINT : Think backwards !

19. copyright©amberpasillas2010 Rewrite so there is NO negative exponent. HINT : Think backwards !

20. copyright©amberpasillas2010 Rewrite so there is NO negative exponent. 2222 = 16 HINT : Think backwards !

21. copyright©amberpasillas2010 Rewrite so there is NO negative exponent. HINT : Think backwards !

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

23. copyright©amberpasillas2010 Exponents and Parenthesis #7 Factored Form 8 x x x Exponential Form 8x 3 4(xy)(xy) 4(xy) 2 (8x) 3 (8x)(8x)(8x) = 8 3 x 3 = 4 x 2 y 2 (5x 3 ) 2 (5 x x x)(5 x x x) = 25x 6 (2y 2 z) 2 (2 y y z) (2 y y z) = 2 2 y 4 z 2 = 512x 3 = 5 2 (x 3 ) 2 = 4y 4 z 2

24. copyright©amberpasillas2010 Fractions With Exponents # 8

25. copyright©amberpasillas2010 Negative Exponent Examples # 9

26. EXTRAS: You can use these extra slides if you are taking a positive exponent and writing it as a negative exponent. copyright©amberpasillas2010

27. Rewrite so there is a negative exponent. HINT: Think backwards!

28. copyright©amberpasillas2010 Rewrite so there is a negative exponent. HINT: Think backwards!

29. copyright©amberpasillas2010 Rewrite so there is a negative exponent. HINT: Think backwards!

30. copyright©amberpasillas2010 Rewrite so there is a negative exponent. HINT: Think backwards!

31. copyright©amberpasillas2010 Rewrite so there is a negative exponent. HINT: Think backwards!

32. copyright©amberpasillas2010 Rewrite so there is a negative exponent. HINT: Think backwards!

33. copyright©amberpasillas2010 Just flip the fraction over to make the exponent positive ! #?