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# Feb. 14th, 2014

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### Feb. 14th, 2014

1. 1. February 14, 2014 Warm-Up Intro to Exponents, Monomials & Scientific Notation
2. 2. At the V6Math Site: For Explanations, Learning Concepts: * purplemath.com* wowmath.org For Practice Problems: * khanacademy.org * braingenie.ck12.com
3. 3. Vocabulary & Formulas Section of Notebook
4. 4. Introduction to Monomials: Exponents
5. 5. Introduction to Monomials: Exponents
6. 6. Introduction to Monomials: Exponents
7. 7. Introduction to Monomials: Exponents
8. 8. Introduction to Monomials: Exponents
9. 9. Introduction to Monomials: Exponents
10. 10. Introduction to Monomials: Exponents
11. 11. Introduction to Monomials: Exponents Practice Problems 1. 72 2. (-8)2 3. (-9) 3 4. -24 5. -43
12. 12. Exponent Laws
13. 13. Exponent Laws
14. 14. Exponent Laws Simplify to lowest terms:
15. 15. Scientific Notation
16. 16. Scientific Notation
17. 17. Scientific Notation
18. 18. Scientific Notation
19. 19. Scientific Notation Write 32.500 in Scientific Notation
20. 20. Scientific Notation
21. 21. Scientific Notation Write the following in Scientific Notation: .00458 = 4.58 • 10 - 3
22. 22. Scientific Notation
23. 23. Scientific Notation
24. 24. Scientific Notation
25. 25. Negative and Zero Exponents Take a look at the following problems and see if you can find the pattern. The expression a-n is the reciprocal of an Examples:
26. 26. Negative and Zero Exponents *Any number (except 0) to the zero power is equal to 1. Negative Exponents Example 1 Example 2 Since 2/3 is in parenthesis, we must apply the power of a quotient property and raise both the 2 and 3 to the negative 2 power. First take the reciprocal to get rid of the negative exponent. Then raise (3/2) to the second power.
27. 27. Negative and Zero Exponents Example 3 Step 1: Step 2: Step 3:
28. 28. Negative and Zero Exponents Example 4: Step 1:
29. 29. Step 2: Step 3: Step 4:
30. 30. Step 5: Step 6-7:
31. 31. Practice Problems
35. 35. Warm- Up Exercises 1. A board 28 feet long is cut into two pieces. The ratio of the lengths of the pieces is 5:2. What are the lengths of the two pieces? 5:7 = X:28; x1 = 20 ft., x2 = 8 feet. 2. The ratio of the length to the width of a rectangle is 5:2. The width is 24 inches long. Find the length. 5:2 = x: 24; Length = 60" 3. What is: 5 6 • 5 - 2 = 5 4 ; 625
36. 36. Warm- Up Exercises 4. (12) -5 • (12) 3 Since the bases are the same (12): the exponents are added. -5 + 3 = -2; (12)-2 = 1/12 2 = 1/144 5. 42 • 35 • 24 43 • 35 • 22 = 22 4 =1 6. Simplify: 5b • 6a4 a c = 30ba4 c
37. 37. Scientific Notation
38. 38. Scientific Notation
39. 39. Scientific Notation
40. 40. Scientific Notation
41. 41. Scientific Notation
42. 42. Scientific Notation
43. 43. Scientific Notation
44. 44. Scientific Notation
45. 45. Monomials Definition: Mono-- The prefix means one. A monomial is an expression with one term. In the equations unit, we said that terms were separated by a plus sign or a minus sign! Therefore: A monomial CANNOT contain a plus sign (+) or a minus (-) sign!
46. 46. Monomials Examples of Monomials:
47. 47. Multiplying Monomials When you multiply monomials, you will need to perform two steps: •Multiply the coefficients (constants) •Multiply the variables A simple problem would be: (3x2)(4x4) And the answer is: 12x6 Remember, the bases are the same, so you add the exponents
48. 48. Multiplying Monomials
49. 49. Multiplying Monomials
50. 50. Multiplying Monomials
51. 51. Multiplying Monomials
52. 52. Multiplying Monomials
53. 53. Multiplying Monomials Now, complete the rest of the problem.
54. 54. Multiplying Monomials
55. 55. Multiplying Monomials
56. 56. Multiplying Monomials Answers 1. (3x5y 2 ) (-5x3y 6 ) Multiply the coefficients. Then multiply the variables (add the exponents of like variables). -15x 8 y 8 2.(-2r3s7t4 )2 (-6r2t 6) Raise the 1st monomial to the 2nd power. (4r6s14t8) (-6r2t 6): Multiply the coefficients and add the variables with like bases = -24r 8s14 t14
57. 57. Multiplying Monomials Answers, con't. 3. (4a2b2c3)3 (2a3b4c2)2 the (64a6b6c9) (4a6b8c4) Raise the 1st monomial to 3rd power and the 2nd monomial to the 2nd power. Multiply the coefficients and add the variables with like bases = 256a12b14c13
58. 58. Dividing Monomials As you've seen in earlier examples, when we work with monomials, we see a lot of exponents. Hopefully you now know the laws of exponents and the properties for multiplying exponents, but what happens when we divide monomials? You probably ask yourself that question everyday.
59. 59. Dividing Monomials Expanded Form Examples When you divide powers that have the same base, you subtract the exponents. That's a pretty easy rule to remember. It's the opposite of the multiplication rule. When you multiply powers that have the same base, you add the exponents and when you divide powers that have the same base, you subtract the exponents!
60. 60. Dividing Monomials Example 1 Example 2 That's an easy rule to remember. Let's look at one more property. The Power of a Quotient Property. A Quotient is an answer to a division problem. What happens when you raise a fraction (or a division problem) to a power? Remember: A division bar and fraction bar are the same thing.
61. 61. Dividing Monomials Power of a Quotient Example 1 Power of a Quotient Example 2
62. 62. Dividing Monomials Dividing Monomials Practice Problems
63. 63. Dividing Monomials Answer Key
64. 64. Simplifying Monomials Properties of Exponents and Using the Order of Operations • If you have a combination of monomial expressions contained with in grouping symbols (parenthesis or brackets), these should be evaluated first. • Power of a Power Property - (This is similar to evaluating Exponents in the Order of Operations). Always evaluate a power of a power before moving on the problem. Example of Power of a Power: • When you multiply monomial expressions, add the exponents of like bases.
65. 65. Simplifying Monomials Example of Multiplying Monomials Example of Dividing Monomials
66. 66. Simplifying Monomials: Sample Problems
67. 67. Simplifying Monomials: Sample Problems Complete the next step:
68. 68. Simplifying Monomials: Sample Problems Now the next: Try to complete the problem:
69. 69. Simplifying Monomials: Sample Problems
70. 70. Simplifying Monomials: Sample Problems Practice Problems
71. 71. Sample Problem Answers Problem 1
72. 72. Sample Problem Answers Problem 2
73. 73. • x ≤ 4 • 5 -2 If 7 pencils cost \$6.65, write the proportion to find the cost for 4 pencils. 7 = 4 6.65 x = 6.65 x 4 / 7 = \$3.80