Review for MA098
Exponents and Polynomials
Multiply.
1) 5x(8x + 7)
1)
Simplify.
2
2) (10x7 y4 )
2)
Write in scientific notation.
3) 0.00003312
3)
Multiply.
4) 7x6 (6x3 - 8x2 - 10)
4)
5) (4x)(6x6 )(x3 )
5)
6) (-6a 6 b)(-5a 3 b5 )(0)
6)
7) (x - 16)2
7)
8) A computer compiles a program in 2.467 × 10-6 seconds. Write this in decimal notation.
8)
Solve.
Simplify.
9) Evaluate. 4 -2
Solve.
9)
10) The sun radiates energy into space at the rate of 3.9 × 1026 joules per second. How many
joules are emitted in two weeks?
10)
Multiply.
11) (10x2 + 7y2 )2
11)
Write in decimal notation.
12) 1.42 × 105
12)
Multiply.
13) 7a 2 b5 (7a 9 b9 - 11b7 + 5a)
13)
State the degree of the polynomial and whether it is a monomial, a binomial, or a trinomial.
14) -7x
1
14)
Divide.
15)
4x4 - 8x 1
-2x-2
15)
Write in scientific notation.
16) 3776
16)
Multiply.
17) (x - 1)(x - 6)
17)
Perform the indicated operations.
18) (3x - 4) - (6x - 18)
18)
Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
-3
19) (2x-1 y2 z -8 )
19)
Solve the problem.
20) The lengths and the widths of the following two rectangles are labeled. Create a
polynomial that describes the sum of the area of these two rectangles.
y
y
3y
18
Write in scientific notation.
21) 0.000152
Simplify.
22)
21)
4
(x 2 )
(6x)3
22)
Multiply.
23) (10x + y)(10x - y)
Divide.
24)
20)
23)
24x9 + 32x4 - 36x2
4x2
24)
Multiply.
25) (7x4 y)(-3x2 y5 )
25)
2
26) (3x + 2y)2
26)
27) (3x + 0.6)(3x - 0.6)
27)
28) The mass of an electron is approximately 9.11 × 10-28 grams. Find the mass of 725,000,000
electrons.
28)
Solve.
Multiply.
29) (-4x4 y)(-9x2 y6 )
29)
State the degree of the polynomial and whether it is a monomial, a binomial, or a trinomial.
30) -18x - 5
30)
31) -13x4
31)
32) If the mass of an object is 4.09144 × 10-7 tons and its density is 5.14 × 10-4 tons per cubic
M
foot, find the volume of this object. (Use the formula D =
and round to the nearest
V
32)
Solve.
hundredth, if necessary.)
Multiply.
33) (2x + 7y)(2x - 7y)
33)
34) (x + 3)(x + 3)(x + 3)
34)
35) (3a + 5b)(9a - 12b)
35)
Combine.
36) (6x2 + 19x + 2) + (-4x2 + 10x - 11)
36)
Write in simplest exponent form.
37) x · x · x · x · x · x · x · x
37)
Multiply.
38) (9x + 5y)2
38)
Simplify. Leave your answer in exponent form.
39) (3 10)(3 28)
39)
3
Solve.
40) The average number of DWI arrests in a certain county increases each year. The number of
DWI arrests can be described by the polynomial function
-0.59x3 + 0.59x2 + 57.24x + 4537.6, where x is the number of years since 1993. Estimate the
40)
number of DWI arrests in 2006. Round to the nearest whole number.
Perform the indicated operations.
41) (8x + 6) - (-12x2 - 4x + 6)
42) -
Divide.
43)
41)
1 2 1
2
2
1
2
x - x+ x2 + x 4
3
3
3
2
3
42)
x2 + 9x + 20
x+5
43)
Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero.
130 x5 y2
44)
44)
78x3 y7
Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
(0.0012)(0.003)
45)
45)
0.006
Write in decimal notation.
46) 8.895 × 10-5
46)
Multiply.
47) (1 + x)(1 - x)
47)
Simplify.
7
48) (x8 )
48)
Evaluate by using scientific notation and the laws of exponents. Leave you answer in scientific notation.
(5,000,000)(16,000)
49)
49)
8,000,000,000
Simplify. Express your answer with positive exponents. Assume that all variables are nonzero.
50) x-5
4
50)
Answer Key
Testname: EXPONENTS & POLYNOMIA
1) 40x2 + 35x
2) 100x14y8
3) 3.312 × 10-5
4) 42x9 - 56x8 - 70x6
5) 24x10
6) 0
7) x2 - 32x + 256
8) 0.000002467
1
9)
16
10) 4.71744 × 1032 joules
11) 100x4 + 140x2 y2 + 49y4
12) 142,000
13) 49a 11b14 - 77a 2 b12 + 35a 3 b5
14) monomial, degree 1
15) -2x6 + 4x3
16) 3.776 × 103
17) x2 - 7x + 6
18) -3x + 14
x3 z 24
19)
8y6
20) 3y2 + 18y
21) 1.52 × 10-4
22)
x5
216
23) 100x2 - y2
24) 6x7 + 8x2 - 9
25) -21x6 y6
26) 9x2 + 12xy + 4y2
27) 9x2 - 0.36
28) 6.60475 × 10-19 grams
29) 36x6 y7
30) binomial, degree 1
31) monomial, degree 4
32) 7.96 × 10-4 cubic feet
33) 4x2 - 49y2
34) x3 + 9x2 + 27x + 27
35) 27a 2 + 9ab - 60b2
36) 2x2 + 29x - 9
37) x8
38) 81x2 + 90xy + 25y2
39) 3 38
5
Answer Key
Testname: EXPONENTS & POLYNOMIA
40) 4085
41) 12x2 + 12x
42)
5 2 1
4
x + x12
6
3
43) x + 4
x2
44)
78y5
45) 6 × 10-4
46) 0.00008895
47) 1 - x2
48) x56
49) 1.0 × 101
1
50)
x5
6