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Laws of Exponents

Laws of Exponents. 7-2 through 7-4. What we call expanded notation. What we call expanded notation. What we call expanded notation. Putting it all together…. Putting it all together… =3  3  3  3  3  3. Putting it all together… =3  3  3  3  3  3

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Laws of Exponents

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  1. Laws of Exponents 7-2 through 7-4

  2. What we call expanded notation

  3. What we call expanded notation

  4. What we call expanded notation

  5. Putting it all together…

  6. Putting it all together… • =3 3 3 3 33

  7. Putting it all together… • =3 3 3 3 33 • All told, how many 3’s?

  8. 6, so our final answer, in exponential notation, is… • =3 3 3 3 33 • All told, how many 3’s?

  9. 6, so our final answer, in exponential notation, is… • = • All told, how many 3’s?

  10. Is there a quicker way? • = • All told, how many 3’s?

  11. Is there a quicker way? • = • All told, how many 3’s? Absolutely; we can gain the same answer by

  12. Is there a quicker way? • = • All told, how many 3’s? Absolutely; we can gain the same answer by adding exponents.

  13. Giving us our 1st law: • Is there a quicker way? • = • All told, how many 3’s? Absolutely; we can gain the same answer by adding exponents.

  14. Giving us our 1st law:

  15. Giving us our 1st law: - When we multiply powers with the same base, we add their individual exponents.

  16. Examples:

  17. Examples:

  18. Examples:

  19. Examples:

  20. Make sure to differentiate between…

  21. Make sure to differentiate between… Exponents and Coefficients

  22. Make sure to differentiate between… Exponents and Coefficients Students will often get mixed up and apply the wrong operation to the problem.

  23. Example of what I mean…

  24. Example of what I mean… 4(9) = 36

  25. Example of what I mean… 4(9) = 36

  26. Example of what I mean… 4(9) = 36

  27. Example of what I mean… 4(9) = 36

  28. Example of what I mean… =

  29. Example of what I mean… =

  30. Example of what I mean… = 6(9) = 54

  31. Example of what I mean… = 6(9) = 54

  32. You try…

  33. You try…

  34. First steps into…

  35. First steps into… Scientific Notation!!!

  36. First steps into…

  37. First steps into… 1 < |a| < 10

  38. First steps into… 1 < |a| < 10 n is an integer.

  39. Examples: 256,000 0.0041

  40. Examples: 256,000 0.0041

  41. Examples: 256,000 0.0041

  42. Keep in mind:

  43. Keep in mind: • a is negative when the original number is negative.

  44. Keep in mind: • a is negative when the original number is negative. • With small decimals, the absolute value of the exponent is equal to the # of zeroes, if you include a lead zero before the decimal place.

  45. Real world application:

  46. Real world application: • At 20 Celsius, one of water has a mass of about 9.98  grams.

  47. Real world application: • At 20 Celsius, one of water has a mass of about 9.98  grams. Each gram of water contains about 3.34  molecules of water

  48. Real world application: • At 20 Celsius, one of water has a mass of about 9.98  grams. Each gram of water contains about 3.34  molecules of water. How many molecules of water are contained in a swimming pool containing 200 of water?

  49. Solution: Dimensional Analysis O =

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