Laws of Exponents

1. This powerpoint will help you when working on “Exponenet Patterning”. Welcome to your personal lesson about the laws of exponents. I hope you enjoy your experience! Here are some things you need to know: 1. You will need a high speed internet connection to take advantage of the whole lesson. 2. When you see this button, it will take you to the base camp (which you will see on the next page). 3. When you see this button, it will take you to the next slide. 4. When you see this button, it will take you back to the slide you just viewed. Laws of Exponents Let’s get started!

2. Base Camp Exponents in Action (Video) I’d rather read about it  Listen and see! Short and sweet- Summary of rules To the Laws! Let’s Play! Practice makes perfect! Sing me the rules Quiz Me! Back to Introduction

3. Video Introducing Exponents Click on the link above. You will be taken to a blog about introducing exponents. In the first paragraph, there is a link to an algebra lesson by NROC Algebra 1—An Open course, Unit 7, Lesson 1, Topic 1: Rules of Exponents. Click on the link. Click on “LOG IN AS GUEST.” On the new webpage, click on the PRESENTATION link.

4. Practice makes perfect! Introducing Exponents • Click on the link above. You will be taken to a blog about introducing exponents. • In the first paragraph, there is a link to an algebra lesson by NROC Algebra 1—An Open course, Unit 7, Lesson 1, Topic 1: Rules of Exponents. Click on the link. • Click on “LOG IN AS GUEST.” • On the new webpage, click on the WORKED EXAMPLES link. • After viewing the examples, click on the PRACTICE link.

5. Listen and See Exponent Tutorials Click on the above link to visit a webpage with various tutorials about the different laws of exponents. Explore any or all of them for better understanding!

6. Exponent Game Exponent Battleship

7. Exponent Song Sing me the Rules!

8. Reading Let's Learn the Exponential Laws

9. Quiz Me! Quiz #1 Quiz #2 Quiz #3 • For QUIZ #3, click on the link above. You will be taken to a blog about introducing exponents. • In the first paragraph, there is a link to an algebra lesson by NROC Algebra 1—An Open course, Unit 7, Lesson 1, Topic 1: Rules of Exponents. Click on the link. • Click on “LOG IN AS GUEST.” • On the new webpage, click on the REVIEW link.

10. Laws of Exponents Law 1 Law 4 Law 7 Law 2 Law 5 Law 8 Law 3 Law 6 Law 9

11. Law 1 Any number raised to the power of 1 equals itself. x1 = x Back to the laws! Show me more!

12. Law 1 - examples x1 = x 101 = 10 61 = 6 1291 = 129 31 = 3 z1 = z b1 = b y1 = y t1 = t Back to the laws!

13. My turn to practice. Law: x1 = x Q1: 81 = ? 1 9 8 7 Back to the laws!

14. Great job! You did it! That’s right! Any number raised to the power of one is itself, so 81 = 8. On to the next problem! Back to the laws!

15. My turn to practice. Law: x1 = x Q2: r1 = ? s r 1 t Back to the laws!

16. Super! That’s right! Any number raised to the power of one is itself, so r1 = r. Back to the laws! On to the next law!

17. Oops! Try again! Remember, any number raised to the power of one is itself! Back to the problem!

18. Law 2 Any number (except 0) raised to the power of 0 equals 1. x0 = 1 Back to the laws! Show me more!

19. Law 2 - examples x0 = 1 100 = 1 60 = 1 1290 = 1 30 = 1 z0 = 1 b0 = 1 y0 = 1 t0 = 1 Back to the laws!

20. My turn to practice. Law: x0 = 1 Q1: 80 = ? 1 0 8 80 Back to the laws!

21. Yay! That’s right! Any number raised to the power of zero is 1, so 80 = 1. On to the next problem! Back to the laws!

22. My turn to practice. Law: x0 = 1 Q2: t0 = ? s 10 t 1 Back to the laws!

23. Good job! That’s right! Any number raised to the power of zero is 1, so t0 = 1. Back to the laws! On to the next law!

24. Not yet! Try again! Remember, any number raised to the power of zero is 1. Back to the problem!

25. Law 3 Any number raised to the power of -1 equals its reciprocal (multiplicative inverse). x-1 = 1/x where x ≠ 0 Back to the laws! Show me more!

26. Law 3 - examples x-1 = 1/x where x ≠ 0 10-1 = 1/10 6-1= 1/6 129-1 = 1/129 3-1= 1/3 z-1 = 1/z b-1 = 1/b y-1= 1/y t-1= 1/t Back to the laws!

27. My turn to practice. Law: x-1 = 1/x Q1: 4-1 = ? 41 1/4 14 -4 Back to the laws!

28. You did it! That’s right! Any number raised to the power of -1 is 1 over itself (its reciprocal), so 4-1 = 1/4. On to the next problem! Back to the laws!

29. My turn to practice. Law: x-1 = 1/x Q2: z-1 = ? z z/z -z 1/z Back to the laws!

30. Looking good! That’s right! Any number raised to the power of -1 is one over itself (its reciprocal), so z-1 = 1/z. Back to the laws! On to the next law!

31. Think again! Remember, any number raised to the power of -1 is 1 over itself (its reciprocal). Back to the problem!

32. Law 4 Any number raised to a power multiplied by that same number raised to another power equals the same number raised to the sum of the powers. xmxn= xm+n Back to the laws! Show me more!

33. Law 4 - examples xmxn= xm+n 104•105 = 109 63•67 = 610 1292•1295 = 1297 36•38 = 314 x5x8 = x13 b2b4 = b6 y1y4 = y5 t2t3 = t5 Back to the laws!

34. My turn to practice. Law: xmxn = xm+n Q1: 52•58 = ? 510 1028 1010 2510 Back to the laws!

35. Yippee! That’s right! Any number raised to a power multiplied by the same number raised to another power is equal to that same number raised to the sum of the powers. So, 52•58 = 510 On to the next problem! Back to the laws!

36. My turn to practice. Law: xmxn = xm+n Q2: v3•v6 = ? v18 v9 v3 v36 Back to the laws!

37. Not quite! Remember, any number raised to a power multiplied by the same number raised to another power is equal to that same number raised to the sum of the powers. Back to the problem!

38. Couldn’t be better! That’s right! Any number raised to a power multiplied by the same number raised to another power is equal to that same number raised to the sum of the powers. So, v3v6 = v9 Back to the laws! On to the next law!

39. Law 5 Any number raised to a power divided by that same number raised to another power equals the same number raised to the difference of the powers. xm/xn= xm-n Back to the laws! Show me more!

40. Law 5 - examples xm/xn= xm-n 107/105 = 102 63/61 = 62 1294/1292 = 1292 39/35 = 34 x9/x2 = x7 b6/b3 = b3 y8/y4 = y4 t9/t3 = t6 Back to the laws!

41. My turn to practice. Law: xm/xn = xm-n Q1: 57/54 = ? 511 103 574 53 Back to the laws!

42. You are so right! That’s right! Any number raised to a power divided by the same number raised to another power is equal to that same number raised to the difference of the powers. So, 57/54 = 53 On to the next problem! Back to the laws!

43. My turn to practice. Law: xm/xn = xm-n Q2: v8/v6 = ? v86 v14 v2 v10 Back to the laws!

44. Let’s try that again! Remember, any number raised to a power divided by the same number raised to another power is equal to that same number raised to the difference of the powers. Back to the problem!

45. Wow! That’s right! Any number raised to a power divided by the same number raised to another power is equal to that same number raised to the difference of the powers. So, v8/v6 = v2 Back to the laws! On to the next law!

46. Law 6 Any number raised to a power then raised to another power equals the same number raised to the product of the powers. (xm)n= xmn Back to the laws! Show me more!

47. Law 6 - examples (xm)n= xmn (107)5 = 1035 (63)4 = 612 (1292)5 = 12910 (36)8 = 348 (x2)7 = x14 (b3)5 = b15 (y7)3 = y21 (t9)1 = t9 Back to the laws!

48. My turn to practice. Law: (xm)n = xmn Q1: (57)3 = ? 510 353 521 157 Back to the laws!

49. You’ve got it! That’s right! Any number raised to a power then raised to another power is that same number raised to the product of the powers. So, (57)3 = 521 On to the next problem! Back to the laws!

50. My turn to practice. Law: (xm)n = xmn Q2: (v4)8 = ? v48 v4 v12 v32 Back to the laws!