WARM-UP:
Write in Standard Form:
                        0
              −426 
1. (−5) 2.
        3
                   ...
WARM-UP:
Write in Standard Form:
                        0
              −426 
1. (−5) 2.
        3
                   ...
WARM-UP:
Write in Standard Form:
                        0
              −426 
1. (−5) 2.
        3
                   ...
WARM-UP:
Write in Standard Form:
                        0
              −426 
1. (−5) 2.
        3
                   ...
WARM-UP:
Write in Standard Form:
                        0
              −426 
1. (−5) 2.
        3
                   ...
WARM-UP:
Write in Standard Form:
                        0
              −426 
1. (−5) 2.
        3
                   ...
WARM-UP:
Write in Standard Form:
                         0
               −426 
1. (−5) 2.
        3
                 ...
WARM-UP:
Write in Standard Form:
                         0
               −426 
1. (−5) 2.
        3
                 ...
3.8 LAWS OF EXPONENTS
         Essential Question:
   What are the laws of exponents?
PRODUCT RULE:
       m   n     m +n
       a ⋅a =a



€
PRODUCT RULE:
                   m   n    m +n
                  a ⋅a =a
What does this mean?

        €
PRODUCT RULE:
                        m   n      m +n
                      a ⋅a =a
What does this mean? 8 2 ⋅ 8 3 =

    ...
PRODUCT RULE:
                          m    n      m +n
                        a ⋅a =a
What does this mean? 8 2 ⋅ 8 3 = ...
PRODUCT RULE:
                          m     n     m +n
                        a ⋅a =a
What does this mean? 8 2 ⋅ 8 3 = ...
PRODUCT RULE:
                          m     n     m +n
                        a ⋅a =a
What does this mean? 8 2 ⋅ 8 3 = ...
QUOTIENT RULE:
        m   n    m−n
       a ÷a =a



€
QUOTIENT RULE:
                       m   n   m−n
                   a ÷a =a

What does this mean?

         €
QUOTIENT RULE:
                     m       n   m−n
                   a ÷a =a

What does this mean? 5 ÷ 5 =
             ...
QUOTIENT RULE:
                       m       n   m−n
                   a ÷a =a
                              5⋅ 5⋅ 5
Wha...
QUOTIENT RULE:
                       m       n       m−n
                   a ÷a =a
                              5⋅ 5⋅ 5...
QUOTIENT RULE:
                       m       n       m−n
                   a ÷a =a
                              5⋅ 5⋅ 5...
QUOTIENT RULE:
                       m       n       m−n
                   a ÷a =a
                              5⋅ 5⋅ 5...
QUOTIENT RULE:
                       m       n       m−n
                   a ÷a =a
                              5⋅ 5⋅ 5...
QUOTIENT RULE:
                       m       n       m−n
                   a ÷a =a
                              5⋅ 5⋅ 5...
QUOTIENT RULE:
                       m       n   m−n
                   a ÷a =a
                              5⋅ 5⋅ 5   5...
POWER RULE:
       m n       m⋅ n
      (a ) = a



€
POWER RULE:
                       m n    m⋅ n
                   (a ) = a
What does this mean?


         €
POWER RULE:
                     m n      m⋅ n
                  (a ) = a
                      2 3
What does this mean? (...
POWER RULE:
                          m n      m⋅ n
                        (a ) = a
                             2 3
What...
POWER RULE:
                          m n      m⋅ n
                        (a ) = a
                             2 3
What...
POWER RULE:
                          m n      m⋅ n
                        (a ) = a
                            2 3
What ...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) =        4




2. (3t)   2
              ⋅ (3t) =            4




3. (2m) ÷ (...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                =

2....
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4               3+4
                                                 ...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4               3+4
                                                 ...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4               3+4
                                                 ...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
EXAMPLES:

1. (−2)   3
              ⋅ (−2) = (−2)   4           3+4
                                                = (−2...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
SUMMARIZER:
 Some calculations are done correctly and some are not.
           Find the errors and correct them.
1. 34 34 ...
HOMEWORK:



page 138-139 #16-51
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Integrated 3.8

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  • Integrated 3.8

    1. 1. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
    2. 2. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
    3. 3. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
    4. 4. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
    5. 5. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
    6. 6. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659
    7. 7. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659 2 2.8561⋅10
    8. 8. WARM-UP: Write in Standard Form: 0  −426  1. (−5) 2. 3    1038  3. (−765)1 4. 4.281⋅10 6 5. 3.112 ⋅10 −3 -125 1 -765 4,281,000 0.003112 € € € € Write in Scientific Form: 6. 285.61 7. 0.08659 2 −2 2.8561⋅10 8.659 ⋅10 €
    9. 9. 3.8 LAWS OF EXPONENTS Essential Question: What are the laws of exponents?
    10. 10. PRODUCT RULE: m n m +n a ⋅a =a €
    11. 11. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? €
    12. 12. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = € €
    13. 13. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = € € €
    14. 14. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = 8 5 € € € €
    15. 15. PRODUCT RULE: m n m +n a ⋅a =a What does this mean? 8 2 ⋅ 8 3 = 8 ⋅ 8 ⋅ 8 ⋅ 8 ⋅ 8 = 8 5 € €If you are MULTIPLYING €the SAME BASE have € then ADD THE EXPONENTS
    16. 16. QUOTIENT RULE: m n m−n a ÷a =a €
    17. 17. QUOTIENT RULE: m n m−n a ÷a =a What does this mean? €
    18. 18. QUOTIENT RULE: m n m−n a ÷a =a What does this mean? 5 ÷ 5 = 3 2 € €
    19. 19. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 € € €
    20. 20. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
    21. 21. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
    22. 22. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = 5⋅ 5 5⋅ 5 € € € €
    23. 23. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 5⋅ 5 5⋅ 5 € € € €
    24. 24. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 =5 5⋅ 5 5⋅ 5 € € € €
    25. 25. QUOTIENT RULE: m n m−n a ÷a =a 5⋅ 5⋅ 5 5⋅ 5⋅ 5 What does this mean? 3 5 ÷5 = 2 = =51 =5 5⋅ 5 5⋅ 5 € € If you are DIVIDING € € have the SAME BASE then SUBTRACT THE EXPONENTS
    26. 26. POWER RULE: m n m⋅ n (a ) = a €
    27. 27. POWER RULE: m n m⋅ n (a ) = a What does this mean? €
    28. 28. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = € €
    29. 29. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = € € €
    30. 30. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = 8 6 € € € €
    31. 31. POWER RULE: m n m⋅ n (a ) = a 2 3 What does this mean? (8 ) = (8 ⋅ 8) ⋅ (8 ⋅ 8) ⋅ (8 ⋅ 8) = 8 6 € If you have a€ POWER to a POWER € € then MULTIPLY THE EXPONENTS
    32. 32. EXAMPLES: 1. (−2) 3 ⋅ (−2) = 4 2. (3t) 2 ⋅ (3t) = 4 3. (2m) ÷ (2m) = 9 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
    33. 33. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = 2. (3t) 2 ⋅ (3t) = 4 €9 3. (2m) ÷ (2m) = 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
    34. 34. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = 4 €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 4 2 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
    35. 35. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 2 € 4 = 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
    36. 36. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 4. ((3k) ) 2 € 4 = € 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
    37. 37. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = 4. ((3k) ) 2 € 4 = € € 5. ((−2) ) 3 4 = 6. (−4) ÷ (−4) = 8 3
    38. 38. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. ((3k) ) 2 € 4 = € € € 5. ((−2) 3 ) 4 = 6. (−4) ÷ (−4) = 8 3
    39. 39. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = € € 5. ((−2) 3 ) 4 = € 8 6. 3 (−4) ÷ (−4) =
    40. 40. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € € 5. ((−2) 3 ) 4 = € 8 €3 6. (−4) ÷ (−4) =
    41. 41. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 1 = (2m) = (2m) 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 ((−2) 3 ) = € 8 €3 6. (−4) ÷ (−4) = €
    42. 42. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. (−4) ÷ (−4) = € €
    43. 43. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. 8−3 (−4) ÷ (−4) = (−4) = € €
    44. 44. EXAMPLES: 1. (−2) 3 ⋅ (−2) = (−2) 4 3+4 = (−2) 7 2. (3t) 2 ⋅ (3t) = (3t) 4 2+4 = (3t) 6 €9 € 3. (2m) ÷ (2m) = 8 (2m) 9−8 = (2m) = (2m)1 4. 2 ((3k) € 4 ) € = (3k) 4⋅ 2 = (3k) 8 € 5. = (−2) 3⋅ 4 € 4 12 ((−2) 3 ) = (−2) € 8 €3 6. 8−3 (−4) ÷ (−4) = (−4) = (−4) 5 € €
    45. 45. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
    46. 46. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
    47. 47. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
    48. 48. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
    49. 49. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 5. (3x)0 = 0 6. 5-2 = -25
    50. 50. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 6. 5-2 = -25
    51. 51. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 6. 5-2 = -25
    52. 52. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25
    53. 53. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25 incorrect
    54. 54. SUMMARIZER: Some calculations are done correctly and some are not. Find the errors and correct them. 1. 34 34 = 67 incorrect 38 2. (132)7 = 1314 correct 3. 109 / 102 = 107 correct 4. (9x)7 / (9x)7 = 1 correct 5. (3x)0 = 0 incorrect 1 6. 5-2 = -25 incorrect 1 / 25
    55. 55. HOMEWORK: page 138-139 #16-51

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