Use the power rules for exponents to simplify. Write the answer in exponential form.
99)
(–23)6
99)
A)
29
B)
–29
C)
–218
D)
218
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
100)
(64)3
62
100)
A)
610
B)
65
C)
614
D)
69
A
Perform the indicated operation.
101)
Subtract (3a3– 3a2) from the sum of (3a3+ 5a2) and (5a3+ 9a2).
101)
A)
5a6+ 17a4
B)
22a10
C)
22a5
D)
5a3+ 17a2
D
Determine the number of terms and name the coefficients of the terms.
102)
3y – 2w– s
102)
A)
3; 3, 2, –1
B)
3; 3, –2, –1
C)
3; 3, –2, 1
D)
3; 3, 2, 1
B
Simplify. Assume that x and y are nonzero.
103)
(5x2y)2(xy2)3
(xy)3
103)
A)
5x7y8
B)
25x2y5
C)
5x4y5
D)
25x4y5
D
D
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
104)
11z4+ 1z3– 3z2+ 9
104)
A)
Trinomial, degree 9
B)
Binomial, degree 10
C)
None, degree 4
D)
Trinomial, degree 4
Identify the base and the exponent for the exponential expression.
105)
y13
105)
A)
Base: 13, exponent: y
B)
Base: 13, exponent: 13y
C)
Base: 13y, exponent: 13
D)
Base: y, exponent: 13
D
Evaluate the expression.
106)
9–1+ 5–1
106)
A)
1
4
B)
45
14
C)
14
45
D)
2
C
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
107)
p2
p–7
107)
A)
1
p9
B)
p9
C)
p–5
D)
p–9
B
C
Solve the problem.
108)
Determine a polynomial that represents the area of the figure.
3x –4
3x +4
108)
A)
9x2+16
B)
9x2–24x +16
C)
9x2+24x –16
D)
9x2–16
Write the number without exponents.
109)
7.12 × 106
109)
A)
71,200,000
B)
427.2
C)
7,120,000
D)
712,000
Find the product.
110)
(7 m + 1 )2
110)
A)
7 m2+ 14m + 1
B)
7 m2+ 1
C)
49 m2+ 14 m + 1
D)
49 m2+ 1
Solve the problem. Express the answer in scientific notation to two decimals.
111)
A computer can do one calculation in 1.4 × 10–7 seconds. How long would it take the computer to
do a trillion (1012) calculations?
111)
A)
1.4 × 105 sec
B)
1.4 × 1012 sec
C)
1.4 × 106 sec
D)
1.4 × 10–7 sec
Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.
112)
x4·x5·x6
112)
A)
x9
B)
x26
C)
x15
D)
x11
Evaluate the expression.
113)
(–7)0
113)
A)
0
B)
7
C)
1
D)
–1
Find the product.
114)
–10x3(–4x6+ 5x3– 8)
114)
A)
40x9– 50x6
B)
40x9+ 5x3– 8
C)
40x6– 50x3+ 80
D)
40x9– 50x6+ 80x3
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
115)
2
5r3+1
5r2
115)
A)
Trinomial, degree 2
B)
Binomial, degree 5
C)
Binomial, degree 2
D)
Binomial, degree 3
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
116)
(4r)7(4r)–6
116)
A)
16r13
B)
4r
C)
1
4r
D)
16r
Find the product.
117)
(8 a – 3 )2
117)
A)
8 a2– 48 a + 9
B)
64 a2– 48 a + 9
C)
8 a2+ 9
D)
64 a2+ 9
Write the number in scientific notation.
118)
6,900,000
118)
A)
6.9 × 106
B)
6.9 × 107
C)
6.9 × 10–6
D)
6.9 × 10–7
Solve the problem.
119)
Find an expression that represents the area of the figure.
2s3
8s4
119)
A)
8s12
B)
8s7
C)
16s12
D)
16s7
Perform the division.
120)
(8m9n –14m8n4+12m7n6) ÷ (2m6n)
120)
A)
19
B)
4m15 –7m14n5+6m13n7
C)
4m3–7m2n3+6mn5
D)
4m3–14m8n4+12m7n6
25
Find the product.
121)
(9y + x)(9y – x)
121)
A)
81y2+ 18xy – x2
B)
81y2– x2
C)
81y2– 18xy – x2
D)
18y2– x2
Find the value of the polynomial.
122)
–4x3+ 4x2– x – 22 when x = – 2
122)
A)
18
B)
16
C)
4
D)
28
D
Provide an appropriate response.
123)
Decide whether the expression is positive, negative, or zero. 1 –560
123)
A)
Positive
B)
Negative
C)
Zero
C
Evaluate the expression.
124)
–3–4
124)
A)
–1
81
B)
81
C)
1
12
D)
–81
A
Use the power rules for exponents to simplify. Write the answer in exponential form.
125)
p
q
7 (q
0)
125)
A)
p
q7
B)
7p
7q
C)
p7
q7
D)
p7
q
C
Graph the equation by completing the table of values.
26
B
126)
y =2x2+ 1
x y
–2
–1
0
1
2
126)
A)
x y
–24.5
–1 2
00.5
1 0
20.5
B)
x y
–2 1
–1–0.5
0–1
1–0.5
2 1
C)
x y
–2 9
–1 3
0 1
1 3
2 9
D)
x y
–2–9
–1–3
0–1
1–3
2–9
Determine whether or not the number is written in scientific notation.
127)
0.0005
127)
A)
in scientific notation
B)
not in scientific notation
Evaluate the expression.
128)
6–1+ 7–1
128)
A)
2
B)
– 1
C)
42
13
D)
13
42
Perform the indicated operation.
129)
(x –4)(x +9)
129)
A)
x2–13x –36
B)
x2– 5x +36
C)
x2+ 5x –36
D)
x2– 5x –4
Perform the division.
130)
15x3– 16x2– 21x + 10
3x – 5
130)
A)
x2– 3x + 2
B)
5x2+ 3x – 2
C)
5x2– 2
D)
x2+ 3x – 2
Add like terms, if possible, and write the result in descending powers of the variable.
131)
8a8– 8a8+ 14a5+ 7a8– 10a5
131)
A)
11a8
B)
11a13
C)
7a8+ 4a5
D)
Cannot be simplified
Perform the indicated operation.
132)
2x2(–3x3–5x2+9x –7)
132)
A)
–6x5–5x2+9x –7
B)
–6x5–10x4+18x3–14x2
C)
–6x6–10x4+18x2–14x2
D)
–12x2
28
Perform the division. Write the answer with positive exponents.
133)
30x7+ 42x6+ 30x4+ 12x2
6x4
133)
A)
–5x3– 7x2– 5 –2
x2
B)
5x3+ 9x2+ 5
C)
5x3+ 7x2+ 5 +2
x2
D)
5x3+ 7x2+ 5
Evaluate the expression.
134)
04
(–4)0
134)
A)
1
B)
–1
C)
–4
D)
0
Find the product.
135)
–7x7(6x8– 2x7+ 9)
135)
A)
–42x8+ 14x7– 63
B)
–42x15 – 2x7+ 9
C)
–42x15 + 14x14 – 63x7
D)
–42x15 + 14x14 + 9
Use the product rule, if possible, to simplify the expression. Write the answer in exponential form.
136)
62·68
136)
A)
3610
B)
3616
C)
616
D)
610
Find the product.
137)
7x3(7x6– 1)
137)
A)
49x6– 7
B)
42x3
C)
49x9– 1
D)
49x9– 7x3
138)
(–5x2)(–9x3)
138)
A)
–14x5
B)
–45x6
C)
–14x6
D)
45x5
Perform the division.
139)
(x2– 4) ÷ (x + 2)
139)
A)
x + 4
B)
x – 4
C)
x2– 2
D)
x – 2
Simplify the expression.
140)
(–2x5y)2
140)
A)
(–2)2x10y2
B)
–4x5y2
C)
–4x5y
D)
(–2)2x7y2
Perform the indicated operation.
141)
(9m + 2)(5m2+ m – 6)
141)
A)
45m3+ 19m2– 52m – 12
B)
45m3+ 1m2– 52m – 12
C)
45m3– 52m – 12
D)
14m2– 52m – 12
30
Perform the division.
142)
64x7+ 24x6+ 40x4+ 64x2
8x4
142)
A)
8x3+ 3x2+ 5
B)
–8x3– 3x2– 5 –8
x2
C)
8x3+ 3x2+ 5 +8
x2
D)
8x3+ 11x2+ 5
Provide an appropriate response.
143)
Is it true that in order to multiply a number by a positive power of ten, you must move the decimal
point to the left as many places as indicated by the exponent on the ten?
143)
A)
Yes
B)
No
Add.
144)
(2 – 5x5+ 4x7– 8x6) + (2x6– 5x5+ 8 + 5x7)
144)
A)
4x7+ 4x6+ 12x5– 3
B)
9x7– 6x6– 10x5+ 10
C)
–7x36 + 10
D)
9x14 – 6x12 – 10x10 + 10
Solve the problem.
145)
Find a polynomial that represents the area of the shaded region.
145)
A)
10a2+ 3a
B)
12a2+ 6a
C)
12a2+ 3a
D)
10a2– 1
Provide an appropriate response.
146)
8
x
x 4
Find the total area.
146)
A)
x2+12
B)
x2+32
C)
x2+8x +32
D)
x2+12x +32
Find the product.
147)
2x +1y 2
147)
A)
4x2+2xy+1y2
B)
4x2+4xy +1y2
C)
2x2+4xy +1y2
D)
4x2+1y2
148)
(x + 5 )4
148)
A)
x4+ 20 x3+ 150 x2+ 500 x + 625
B)
x4+ 20 x3+ 150 x2+ 20 x + 625
C)
x4+ 20 x3+ 250 x2+ 500 x + 625
D)
x4+ 5 x3+ 150 x2+ 250 x + 625
32
Perform the division.
149)
(x2+ 3x + 2) ÷ (x + 1)
149)
A)
x2+ 2
B)
x + 2
C)
x + 3
D)
x2+ 3
Evaluate.
150)
(–2)3
150)
A)
2
B)
–8
C)
8
D)
–2
Simplify, and write the answer using only positive exponents. Assume all variables represent nonzero numbers.
151)
3–3·35
3–4
151)
A)
36
B)
277
C)
96
D)
34
Provide an appropriate response.
152)
Determine if the expression 1–7 is positive or negative.
152)
A)
Positive
B)
Negative
Identify the base and the exponent for the exponential expression.
153)
(11x)12
153)
A)
Base: 12, exponent: x
B)
Base: 11x, exponent: 12
C)
Base: 12, exponent: 11x
D)
Base: x, exponent: 12
Write the number in scientific notation.
154)
0.00006402
154)
A)
6.402× 10–5
B)
6.402× 104
C)
6.402× 10–4
D)
6.402× 105
Perform the indicated operation.
155)
(x + 5y)(–5x – 3y)
155)
A)
x2– 28xy – 15y2
B)
–5x2– 28xy – 28y2
C)
–5x2– 28xy – 15y2
D)
x2– 28xy – 28y2
C
Identify the base and the exponent for the exponential expression.
156)
(–6x)3
156)
A)
Base: 6x, exponent: 3
B)
Base: –6x, exponent: 3
C)
Base: x, exponent: 3
D)
Base: 3, exponent: –6x
B
Perform the division. Write the answer with positive exponents.
157)
12x4– 16x3+ 12x2
4x3
157)
A)
3x – 16x3+3
x
B)
3x – 4
C)
3x – 4 +3
x
D)
6x – 4
C
Find the product.
158)
(7 a + 8 c)( 7a – 8 c)
158)
A)
49 a2– 64 c2
B)
49 a2+ 112 ac – 64 c2
C)
49 a2– 112 ac – 64 c2
D)
7 a2– 8 c2
A
34
A
159)
(n + 2 )2
159)
A)
n2+ 4 n + 4
B)
n +4
C)
n2+ 4
D)
4 n2+ 4 n + 4
Write the number using scientific notation.
160)
16,000,000
160)
A)
1.6 × 106
B)
1.6 × 107
C)
1.6 × 10–6
D)
1.6 × 10–7
Write the number in scientific notation.
161)
0.000000465013
161)
A)
4.65013 × 10–6
B)
4.65013 × 107
C)
4.65013 × 106
D)
4.65013 × 10–7
Write the expression using exponents.
162)
1
5·5·5·5
162)
A)
1
5
B)
1
C)
1
20
D)
1
54
Evaluate the expression.
163)
(–4)0–40
163)
A)
0
B)
1
C)
–1
D)
4
Write the quotient without using exponents.
164)
20 × 10–1
5× 10–2
164)
A)
0.008
B)
40
C)
80
D)
0.004
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
165)
t3
t7
165)
A)
t4
B)
t–7
C)
t3
t4
D)
1
t4
Predict the display a calculator would give for the expression shown in the screen.
166)
2990000000000
166)
A)
2.99E–12
B)
2.99E12
C)
29.9E13
D)
29.9E–13
Find the product.
167)
(2m3z4)(5m2z2)
167)
A)
10m5z
B)
10mz6
C)
10mz5
D)
10m5z6
Perform the indicated operation. Write the answer in scientific notation.
168)
16.8 × 10–1
4.0 × 108
168)
A)
8.4 × 107
B)
4.2 × 107
C)
8.4 × 10–9
D)
4.2 × 10–9
Perform the division.
169)
x4+ 8x2+ 10
x2+ 1
169)
A)
x2+ 7x +3
2
B)
x2+ 7 +1
C)
x2+ 7
D)
x2+ 7 +3
x2+ 1
Simplify the expression.
170)
pm4
q3
5
(q
0)
170)
A)
p5m9
q8
B)
pm9
q8
C)
p5m20
q15
D)
pm20
q15
171)
(3p3s2)4(s2)
171)
A)
81p7s16
B)
81p7s8
C)
3p12s10
D)
81p12s10
If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
172)
The speed of light is 1.86 × 105 miles per hour.
172)
A)
1,860,000
B)
.0000186
C)
18,600,000
D)
186,000
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
173)
t8
t
173)
A)
1
t7
B)
t8
C)
t7
D)
t
D)
Find the product.
174)
10x +5
11 10x –5
11
174)
A)
10x2–25
121
B)
100x2+25
121
C)
100x2–100
11 x –25
121
D)
100x2–25
121
D)
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
175)
(y +c)–5
(y +c)–6
175)
A)
1
(y +c)
B)
1
(y +c)11
C)
(y +c)11
D)
y+c
D)
D)