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Rules of Exponents
Simplify.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. Each side of a square measures units. Find the area of the square in terms of x.
12. Each side of a cube measures units. Find the volume of the cube in terms of x.
Introduction to Polynomials
Classify the given polynomial as a monomial, binomial, or trinomial and state the degree.
13.
14.
15.
16. 10
Write the following polynomials in standard form.
17.
18.
Evaluate.
19. , where
20. , where
21. , where , , and
22. , where and
23. , where and
24. , where and
25. Given , find .
26. Given , find .
27. The surface area of a rectangular solid is given by the formula , where l, w, and h represent the length, width, and height, respectively. If the length of a rectangular solid measures 2 units, the width measures 3 units, and the height measures 5 units, then calculate the surface area.
28. The surface area of a sphere is given by the formula , where r represents the radius of the sphere. If a sphere has a radius of 5 units, then calculate the surface area.
Adding and Subtracting Polynomials
Perform the operations.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39. Subtract from .
40. Subtract from .
41. Given and , find .
42. Given and , find .
43. Given and , find .
44. Given and , find .
Multiplying Polynomials
Multiply.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59. Find the product of and .
60. Find the product of and .
61. Given and , find .
62. Given and , find .
63. Given and , find .
64. Given and , find .
Dividing Polynomials
Divide.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79. Given and , find .
80. Given and , find .
81. Given and , find .
82. Given and , find .
Negative Exponents
Simplify.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
The value in dollars of a new laptop computer can be estimated by using the formula , where t represents the number of years after the purchase.
94. Estimate the value of the laptop when it is 1½ years old.
95. What was the laptop worth new?
Rewrite using scientific notation.
96. 2,030,000,000
97. 0.00000004011
Perform the indicated operations.
98.
99.
100.
101.
102. 5,000,000,000,000 × 0.0000023
103. 0.0003/120,000,000,000,000
Simplify.
1.
2.
3.
4. a. ; b.
Evaluate.
5. , where
6. , where and
Perform the operations.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Simplify.
17.
18.
19.
20.
21. Subtract from .
22. If each side of a cube measures units, calculate the volume in terms of x.
23. The height of a projectile in feet is given by the formula , where t represents time in seconds. Calculate the height of the projectile at 1½ seconds.
24. The cost in dollars of producing custom t-shirts is given by the formula , where x represents the number of t-shirts produced. The revenue generated by selling the t-shirts for $6.50 each is given by the formula , where x represents the number of t-shirts sold.
a. Find a formula for the profit. (profit = revenue − cost)
b. Use the formula to calculate the profit from producing and selling 150 t-shirts.
25. The total volume of water in earth’s oceans, seas, and bays is estimated to be cubic feet. By what factor is the volume of the moon, cubic feet, larger than the volume of earth’s oceans? Round to the nearest tenth.
1:
3:
5:
7:
9:
11:
13: Binomial; degree 3
15: Monomial; degree 3
17:
19: 22
21: 6
23: −7
25:
27: 62 square units
29:
31:
33:
35:
37:
39:
41:
43:
45:
47:
49:
51:
53:
55:
57:
59:
61:
63:
65:
67:
69:
71:
73:
75:
77:
79:
81:
83:
85:
87:
89:
91:
93:
95: $1,200
97:
99:
101:
103:
1:
3:
5: 60
7:
9:
11:
13:
15:
17:
19:
21:
23: 118 feet
25: 16.4