1. 6.1 PROPERTIES OF EXPONENTS OBJECTIVE: TO SIMPLIFY EXPRESSIONS USING THE PROPERTIES OF EXPONENTS

2. DO-NOW Evaluate using your calculator: A. 3 8 B. 3 3 C. 10 5

3. DAY 1 PRODUCT OF POWER

4. EXPONENT How many times a number is used as a factor

5. EXAMPLE:

6. LET’S LOOK AT: X 3 X 2

7. PRODUCT-OF-POWERS PROPERTY: To multiply powers with the same base, add their exponents. Algebra: a m a n = a n + m Numbers: 5 2 5 4 = 5 6

8. EXAMPLES: 2. 2 3 2 4 3. 9 9 4 4. y 2 y 3 5. x n x n + 2

9. TRY ON YOUR OWN: A.3 5 3 1 B. Z 6 Z 3 C. a 2 a

10. STEPS TO SIMPLIFY: 1. Multiply constants 2. Use product of powers property to simplify variables

11. EXAMPLES: 6. (5t)(-30t 2 ) 7. (3x 3 z 2 )(-6y 5 ) 8. (-4a 2 b)(-ac 2 )(3b 2 c 2 )

12. TRY ON YOUR OWN: D. (3m 2 )(60mp 2 ) E. (8xz)(-10y)(-2yz 2 )

13. HOMEWORK: PRACTICE WORKSHEET!

14. DO-NOW: A. B. C.

15. DAY 2: POWER OF A POWER (MULTIPLICATION ONLY) COMBINATION OF DAY 1 AND DAY 2

16. (X 2 ) 3= LET’S LOOK AT:

17. POWER-OF-POWERS PROPERTY: To find a power of a power, multiply the exponents Algebra: (a m ) n = a m n Numbers: (5 2)4 = 5 8

18. EXAMPLES: SIMPLIFY 1.2. 3.4.

19. (AB) 3= LET’S LOOK AT:

20. POWER-OF-POWERS PROPERTY: Algebra: (ab) n = a n b n Numbers: (5 6 ) n = 5 n 6 n

21. EXAMPLES: SIMPLIFY 5. 6. 7.

22. POWERS OF -1: Even powers: 1 Odd Powers: -1

23. EXAMPLES: SIMPLIFY 8. (-1) 5 9. (-t 4 ) 2 10. (-3x) 3

24. EXAMPLES: 11. (ab 2 ) 3 (a 3 ) 4 12. (x 5 y 2 ) 3 (xy 8 ) 3

25. HOMEWORK: PRACTICE PROBLEMS AT THE BOTTOM OF THE NOTES

26. DO-NOW: A. B. C. (-1) 5

27. DAY 3 QUOTIENT OF POWERS

28. LET’S LOOK AT:

29. QUOTIENT-OF- POWERS PROPERTY:

30. EXAMPLES: SIMPLIFY 1.2.3.

31. EXAMPLES: SIMPLIFY 4.5.6.

32. POWERS-OF-A-FRACTION: Algebra:

33. EXAMPLES: SIMPLIFY: 7.8.9.

34. EXAMPLES: SIMPLIFY: 10.11.

35. EXAMPLES: SIMPLIFY: 12.13.

36. HOMEWORK: PRACTICE PROBLEMS AT THE BOTTOM OF THE NOTES

37. DO-NOW: Use your calculator to find the following:

38. DAY 4 – ZEROS NEGATIVES

39. ZERO EXPONENTS For any nonzero number a 0 = 1.

40. EXAMPLE 1: EVALUATE EACH EXPRESSION a)b) c)d)

41. NEGATIVE EXPONENTS: USE YOUR CALCULATOR TO EVALUATE THE FOLLOWING:

42. NEGATIVE EXPONENTS: a -n is the reciprocal of a n Algebra: Numbers:

43. EXAMPLE 2: REWRITE WITHOUT NEGATIVE EXPONENTS & EVALUATE IF POSSIBLE a)b)c) d)e)

44. MIXED REVIEW: REWRITE WITHOUT NEGATIVE OR ZERO EXPONENTS a)b) c)d)

45. CLASS WORK: WORK ON 12 PRACTICE PROBLEMS

46. DAY 3.5 – PUT IT ALL TOGETHER

47. 2 ND HALF OF CLASS: WORK ON PRACTICE WS