2. Warm- Up Exercises
1. What is the simplified fraction of 35%?
7/20
2.
3. Order the following from greatest to least:
3.45, 3⅗, 54.3%, 3⅓

3. Warm- Up Exercises
4. Mike painted 120 houses in 4 months. Jack took two
more months to paint the same number of houses. If
they worked together to paint an additional 120 houses,
how many would each paint?
5. Prom tickets cost $10 for singles and $15 for couples.
Fifty more couples tickets were sold than were singles
tickets. Total ticket sales were $4000.
How many of each ticket type were sold?

4. Review of Systems Test
4. Which system of inequality best represents the graph?
A. y > -2 and y > x + 1 B. y < -2 and y > x + 1
C. y > -2 and y < x + 1 D. y < -2 and y < x + 1 E. None
A. y > -2 and y < x + 1 B. y < -2 and y > x + 1
C. y > -2 and y > x + 1 D. y < -2 and y < x + 1 E. None

5. Review of Systems Test
5.
7. What is the solution to the following
system of equations?
A. ( 2, -2 ) B. ( -2, 2 ) C. No Solution
D. Infinite Solutions E. None
A. ( 2, -2 ) B. ( -2, 2 ) C. Infinite Solutions
D. No Solution E. None

6. Review of Systems Test
Which of the following graphs represents the solution
to the following system of inequalities? 6x – 2y < 6 and x - y < -1
A B C
D E. None

7. Vocabulary & Formulas Section of Notebook

8. Introduction to Monomials: Exponents

9. Introduction to Monomials: Exponents

10. Introduction to Monomials: Exponents

11. Introduction to Monomials: Exponents

12. Introduction to Monomials: Exponents

13. Introduction to Monomials: Exponents

14. Introduction to Monomials: Exponents

15. Introduction to Monomials: Exponents
Practice Problems
1. 72
2. (-8)2
3. (-9) 3
4. -24
5. -43

16. Exponent Laws

17. Exponent Laws

21. Exponent Laws
Simplify to lowest terms:

22. Scientific Notation

23. Scientific Notation

24. Scientific Notation

25. Scientific Notation

26. Scientific Notation
Write 32.500 in Scientific Notation

27. Scientific Notation

28. Scientific Notation
Write the following in Scientific Notation:
.00458
= 4.58 • 10 - 3

29. Scientific Notation

30. Scientific Notation

31. Scientific Notation

32. 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:

33. 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.

34. Negative and Zero Exponents
Example 3
Step 1:
Step 2:
Step 3:

35. Negative and Zero Exponents
Example 4:
Step 1:

36. Step 2:
Step 3:
Step 4:

37. Step 5:
Step 6-7:

38. Practice Problems

39. Negative Exponents: Answers

40. Negative Exponents: Answers

41. Negative Exponents: Answers

42. 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

43. 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. 4 2 • 35 • 24
4 3 • 35 • 22
= 22
4 =1
6. Simplify: 5b • 6a4
a c
= 30ba4 c

44. Scientific Notation

45. Scientific Notation

46. Scientific Notation

47. Scientific Notation

48. Scientific Notation

49. Scientific Notation

50. Scientific Notation

51. Scientific Notation

52. 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!

53. Monomials
Examples of Monomials:

54. 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

55. Multiplying Monomials

56. Multiplying Monomials

57. Multiplying Monomials

58. Multiplying Monomials

59. Multiplying Monomials

60. Multiplying Monomials
Now, complete the rest of the problem.

61. Multiplying Monomials

62. Multiplying Monomials

63. 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

64. Multiplying Monomials Answers, con't.
3. (4a2b2c3)3 (2a3b4c2)2
Raise the 1st monomial to the
(64a6b6c9) (4a6b8c4) 3rd power and the 2nd
monomial to the 2nd power.
Multiply the coefficients and add the variables with like bases
= 256a12b14c13

65. 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.

66. 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!

67. 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.

68. Dividing Monomials
Power of a Quotient Example 1
Power of a Quotient Example 2

69. Dividing Monomials
Dividing Monomials Practice Problems

70. Dividing Monomials Answer Key

71. 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.

72. Simplifying Monomials
Example of Multiplying Monomials
Example of Dividing Monomials

73. Simplifying Monomials: Sample Problems

74. Simplifying Monomials: Sample Problems
Complete the next step:

75. Simplifying Monomials: Sample Problems
Now the next:
Try to complete the problem:

76. Simplifying Monomials: Sample Problems

77. Simplifying Monomials: Sample Problems
Practice Problems

78. Sample Problem Answers
Problem 1

79. Sample Problem Answers
Problem 2

80. • 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