February 14,
2014

Warm-Up
Intro to Exponents, Monomials &
Scientific Notation
At the V6Math Site:
For Explanations, Learning Concepts:
* purplemath.com* wowmath.org
For Practice Problems:
* khanacadem...
Vocabulary & Formulas Section of Notebook
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Introduction to Monomials: Exponents
Practice Problems
1. 72
2. (-8)2
3. (-9) 3
4. -24

5. -43
Exponent Laws
Exponent Laws
Exponent Laws
Simplify to lowest terms:
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Write 32.500 in Scientific Notation
Scientific Notation
Scientific Notation
Write the following in Scientific Notation:

.00458
= 4.58 • 10 - 3
Scientific Notation
Scientific Notation
Scientific Notation
Negative and Zero Exponents
Take a look at the following problems and see if you
can find the pattern.

The expression a-n...
Negative and Zero Exponents
*Any number (except 0) to the zero power is equal to 1.
Negative Exponents
Example 1

Example ...
Negative and Zero Exponents
Example 3
Step 1:

Step 2:
Step 3:
Negative and Zero Exponents
Example 4:

Step 1:
Step 2:

Step 3:

Step 4:
Step 5:

Step 6-7:
Practice Problems
Negative Exponents: Answers
Negative Exponents: Answers
Negative Exponents: Answers
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...
Warm- Up Exercises
4.

(12) -5 • (12) 3

Since the bases are the same (12): the exponents are
added. -5 + 3 = -2; (12)-2 =...
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Scientific Notation
Monomials
Definition: Mono-- The prefix means one.
A monomial is an expression with one term.
In the equations unit, we sa...
Monomials
Examples of Monomials:
Multiplying Monomials

When you multiply monomials, you will
need to perform two steps:
•Multiply the coefficients (consta...
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials

Now, complete the rest of the problem.
Multiplying Monomials
Multiplying Monomials
Multiplying Monomials Answers
1. (3x5y 2 ) (-5x3y 6 )
Multiply the coefficients. Then multiply the variables (add
the expo...
Multiplying Monomials Answers, con't.
3. (4a2b2c3)3 (2a3b4c2)2
the (64a6b6c9) (4a6b8c4)

Raise the 1st monomial to
3rd pow...
Dividing Monomials
As you've seen in earlier examples, when we work
with monomials, we see a lot of exponents.
Hopefully y...
Dividing Monomials
Expanded Form Examples

When you divide powers that have the same base, you subtract the
exponents. Tha...
Dividing Monomials
Example 1

Example 2

That's an easy rule to remember. Let's look at one more
property. The Power of a ...
Dividing Monomials
Power of a Quotient Example 1

Power of a Quotient Example 2
Dividing Monomials
Dividing Monomials Practice Problems
Dividing Monomials Answer Key
Simplifying Monomials
Properties of Exponents and Using the Order of Operations
• If you have a combination of monomial ex...
Simplifying Monomials

Example of Multiplying Monomials

Example of Dividing Monomials
Simplifying Monomials: Sample Problems
Simplifying Monomials: Sample Problems

Complete the next step:
Simplifying Monomials: Sample Problems

Now the next:

Try to complete the problem:
Simplifying Monomials: Sample Problems
Simplifying Monomials: Sample Problems

Practice Problems
Sample Problem Answers

Problem 1
Sample Problem Answers

Problem 2
• 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 =...
Feb. 14th, 2014
Feb. 14th, 2014
Feb. 14th, 2014
Feb. 14th, 2014
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
  32. 32. Negative Exponents: Answers
  33. 33. Negative Exponents: Answers
  34. 34. Negative Exponents: Answers
  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
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