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Math Problems
Algebra 1
Multiplication with rational exponents
Which of the following is not equivalent to
sec
3
π
8
\sec \frac{3 \pi}{8}
sec
8
3
π
?
\newline
sec
(
−
3
π
8
)
\sec \left(-\frac{3 \pi}{8}\right)
sec
(
−
8
3
π
)
\newline
sec
19
π
8
\sec \frac{19 \pi}{8}
sec
8
19
π
\newline
sec
5
π
8
\sec \frac{5 \pi}{8}
sec
8
5
π
\newline
sec
13
π
8
\sec \frac{13 \pi}{8}
sec
8
13
π
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Which of the following is not equivalent to
cos
2
π
5
\cos \frac{2 \pi}{5}
cos
5
2
π
?
\newline
cos
7
π
5
\cos \frac{7 \pi}{5}
cos
5
7
π
\newline
cos
8
π
5
\cos \frac{8 \pi}{5}
cos
5
8
π
\newline
cos
12
π
5
\cos \frac{12 \pi}{5}
cos
5
12
π
\newline
cos
(
−
2
π
5
)
\cos \left(-\frac{2 \pi}{5}\right)
cos
(
−
5
2
π
)
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Which of the following is not equivalent to
csc
2
π
7
\csc \frac{2 \pi}{7}
csc
7
2
π
?
\newline
csc
(
−
12
π
7
)
\csc \left(-\frac{12 \pi}{7}\right)
csc
(
−
7
12
π
)
\newline
csc
16
π
7
\csc \frac{16 \pi}{7}
csc
7
16
π
\newline
csc
12
π
7
\csc \frac{12 \pi}{7}
csc
7
12
π
\newline
csc
19
π
7
\csc \frac{19 \pi}{7}
csc
7
19
π
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Which of the following is not equivalent to
tan
2
π
7
\tan \frac{2 \pi}{7}
tan
7
2
π
?
\newline
tan
9
π
7
\tan \frac{9 \pi}{7}
tan
7
9
π
\newline
tan
16
π
7
\tan \frac{16 \pi}{7}
tan
7
16
π
\newline
tan
(
−
12
π
7
)
\tan \left(-\frac{12 \pi}{7}\right)
tan
(
−
7
12
π
)
\newline
tan
19
π
7
\tan \frac{19 \pi}{7}
tan
7
19
π
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Which of the following is equivalent to
sin
π
6
\sin \frac{\pi}{6}
sin
6
π
?
\newline
sin
11
π
6
\sin \frac{11 \pi}{6}
sin
6
11
π
\newline
sin
(
−
π
6
)
\sin \left(-\frac{\pi}{6}\right)
sin
(
−
6
π
)
\newline
sin
7
π
6
\sin \frac{7 \pi}{6}
sin
6
7
π
\newline
sin
(
−
11
π
6
)
\sin \left(-\frac{11 \pi}{6}\right)
sin
(
−
6
11
π
)
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Which of the following is not equivalent to
csc
3
π
8
\csc \frac{3 \pi}{8}
csc
8
3
π
?
\newline
csc
(
−
13
π
8
)
\csc \left(-\frac{13 \pi}{8}\right)
csc
(
−
8
13
π
)
\newline
csc
19
π
8
\csc \frac{19 \pi}{8}
csc
8
19
π
\newline
csc
21
π
8
\csc \frac{21 \pi}{8}
csc
8
21
π
\newline
csc
11
π
8
\csc \frac{11 \pi}{8}
csc
8
11
π
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Which of the following is not equivalent to
cot
π
6
\cot \frac{\pi}{6}
cot
6
π
?
\newline
cot
13
π
6
\cot \frac{13 \pi}{6}
cot
6
13
π
\newline
cot
11
π
6
\cot \frac{11 \pi}{6}
cot
6
11
π
\newline
cot
7
π
6
\cot \frac{7 \pi}{6}
cot
6
7
π
\newline
cot
(
−
11
π
6
)
\cot \left(-\frac{11 \pi}{6}\right)
cot
(
−
6
11
π
)
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Which of the following is not equivalent to
cot
3
π
8
?
\cot \frac{3 \pi}{8} ?
cot
8
3
π
?
\newline
cot
(
−
13
π
8
)
\cot \left(-\frac{13 \pi}{8}\right)
cot
(
−
8
13
π
)
\newline
cot
5
π
8
\cot \frac{5 \pi}{8}
cot
8
5
π
\newline
cot
19
π
8
\cot \frac{19 \pi}{8}
cot
8
19
π
\newline
cot
11
π
8
\cot \frac{11 \pi}{8}
cot
8
11
π
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Which of the following is equivalent to
sin
3
π
7
\sin \frac{3 \pi}{7}
sin
7
3
π
?
\newline
sin
11
π
7
\sin \frac{11 \pi}{7}
sin
7
11
π
\newline
sin
10
π
7
\sin \frac{10 \pi}{7}
sin
7
10
π
\newline
sin
(
−
3
π
7
)
\sin \left(-\frac{3 \pi}{7}\right)
sin
(
−
7
3
π
)
\newline
sin
(
−
11
π
7
)
\sin \left(-\frac{11 \pi}{7}\right)
sin
(
−
7
11
π
)
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Which of the following is equivalent to
sin
π
7
\sin \frac{\pi}{7}
sin
7
π
?
\newline
sin
13
π
7
\sin \frac{13 \pi}{7}
sin
7
13
π
\newline
sin
8
π
7
\sin \frac{8 \pi}{7}
sin
7
8
π
\newline
sin
(
−
π
7
)
\sin \left(-\frac{\pi}{7}\right)
sin
(
−
7
π
)
\newline
sin
15
π
7
\sin \frac{15 \pi}{7}
sin
7
15
π
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Which of the following is equivalent to
cot
π
4
\cot \frac{\pi}{4}
cot
4
π
?
\newline
cot
(
−
π
4
)
\cot \left(-\frac{\pi}{4}\right)
cot
(
−
4
π
)
\newline
cot
7
π
4
\cot \frac{7 \pi}{4}
cot
4
7
π
\newline
cot
3
π
4
\cot \frac{3 \pi}{4}
cot
4
3
π
\newline
cot
(
−
7
π
4
)
\cot \left(-\frac{7 \pi}{4}\right)
cot
(
−
4
7
π
)
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Perform the following operation and express in simplest form.
\newline
x
+
2
6
x
+
30
⋅
x
2
+
11
x
+
30
x
2
+
8
x
+
12
\frac{x+2}{6 x+30} \cdot \frac{x^{2}+11 x+30}{x^{2}+8 x+12}
6
x
+
30
x
+
2
⋅
x
2
+
8
x
+
12
x
2
+
11
x
+
30
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
3
x
2
−
4
x
−
32
⋅
x
2
−
16
6
x
2
\frac{x^{3}}{x^{2}-4 x-32} \cdot \frac{x^{2}-16}{6 x^{2}}
x
2
−
4
x
−
32
x
3
⋅
6
x
2
x
2
−
16
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
−
16
x
2
−
x
−
12
⋅
9
x
+
27
4
x
−
32
\frac{x^{2}-16}{x^{2}-x-12} \cdot \frac{9 x+27}{4 x-32}
x
2
−
x
−
12
x
2
−
16
⋅
4
x
−
32
9
x
+
27
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
+
3
x
−
54
x
3
+
4
x
2
÷
x
2
−
81
x
3
−
9
x
2
\frac{x^{2}+3 x-54}{x^{3}+4 x^{2}} \div \frac{x^{2}-81}{x^{3}-9 x^{2}}
x
3
+
4
x
2
x
2
+
3
x
−
54
÷
x
3
−
9
x
2
x
2
−
81
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
x
2
+
2
x
−
48
÷
x
3
x
2
−
64
\frac{x}{x^{2}+2 x-48} \div \frac{x^{3}}{x^{2}-64}
x
2
+
2
x
−
48
x
÷
x
2
−
64
x
3
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
x
2
−
64
⋅
x
2
−
10
x
+
16
x
−
2
\frac{x^{2}}{x^{2}-64} \cdot \frac{x^{2}-10 x+16}{x-2}
x
2
−
64
x
2
⋅
x
−
2
x
2
−
10
x
+
16
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
−
2
x
−
48
6
x
⋅
x
−
6
x
2
−
36
\frac{x^{2}-2 x-48}{6 x} \cdot \frac{x-6}{x^{2}-36}
6
x
x
2
−
2
x
−
48
⋅
x
2
−
36
x
−
6
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
3
x
2
−
17
x
+
72
⋅
x
2
−
64
3
x
+
24
\frac{x^{3}}{x^{2}-17 x+72} \cdot \frac{x^{2}-64}{3 x+24}
x
2
−
17
x
+
72
x
3
⋅
3
x
+
24
x
2
−
64
\newline
Answer:
Get tutor help
Perform the following operation and express in simplest form.
\newline
x
2
−
64
x
2
−
x
−
72
⋅
4
x
−
36
x
2
+
8
x
\frac{x^{2}-64}{x^{2}-x-72} \cdot \frac{4 x-36}{x^{2}+8 x}
x
2
−
x
−
72
x
2
−
64
⋅
x
2
+
8
x
4
x
−
36
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
−
81
x
2
−
x
−
72
⋅
4
x
+
32
x
+
9
\frac{x^{2}-81}{x^{2}-x-72} \cdot \frac{4 x+32}{x+9}
x
2
−
x
−
72
x
2
−
81
⋅
x
+
9
4
x
+
32
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
−
36
x
2
−
6
x
⋅
x
2
x
2
+
2
x
−
24
\frac{x^{2}-36}{x^{2}-6 x} \cdot \frac{x^{2}}{x^{2}+2 x-24}
x
2
−
6
x
x
2
−
36
⋅
x
2
+
2
x
−
24
x
2
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
−
11
x
+
28
x
2
−
16
⋅
x
2
+
4
x
x
−
4
\frac{x^{2}-11 x+28}{x^{2}-16} \cdot \frac{x^{2}+4 x}{x-4}
x
2
−
16
x
2
−
11
x
+
28
⋅
x
−
4
x
2
+
4
x
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
x
2
−
81
⋅
x
2
+
6
x
−
27
3
x
\frac{x^{2}}{x^{2}-81} \cdot \frac{x^{2}+6 x-27}{3 x}
x
2
−
81
x
2
⋅
3
x
x
2
+
6
x
−
27
\newline
Answer:
Get tutor help
Perform the operation and express your answer as a single fraction in simplest form.
\newline
5
3
x
−
3
x
5
\frac{5}{3 x}-\frac{3 x}{5}
3
x
5
−
5
3
x
\newline
Answer:
Get tutor help
Perform the operation and express your answer as a single fraction in simplest form.
\newline
5
2
−
2
3
x
3
\frac{5}{2}-\frac{2}{3 x^{3}}
2
5
−
3
x
3
2
\newline
Answer:
Get tutor help
Perform the operation and express your answer as a single fraction in simplest form.
\newline
1
y
2
+
1
y
\frac{1}{y^{2}}+\frac{1}{y}
y
2
1
+
y
1
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
x
2
2
⋅
4
x
2
7
\frac{x^{2}}{2} \cdot \frac{4 x^{2}}{7}
2
x
2
⋅
7
4
x
2
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
x
3
3
2
x
2
\frac{\frac{x}{3}}{\frac{3}{2 x^{2}}}
2
x
2
3
3
x
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
8
x
3
5
⋅
2
3
x
2
\frac{8 x^{3}}{5} \cdot \frac{2}{3 x^{2}}
5
8
x
3
⋅
3
x
2
2
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
7
x
5
7
x
6
\frac{\frac{7 x}{5}}{\frac{7 x}{6}}
6
7
x
5
7
x
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
2
x
3
⋅
3
x
2
10
\frac{2 x}{3} \cdot \frac{3 x^{2}}{10}
3
2
x
⋅
10
3
x
2
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
9
5
x
3
⋅
x
6
\frac{9}{5 x^{3}} \cdot \frac{x}{6}
5
x
3
9
⋅
6
x
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
5
x
7
⋅
4
x
2
5
\frac{5 x}{7} \cdot \frac{4 x^{2}}{5}
7
5
x
⋅
5
4
x
2
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
9
x
2
4
⋅
3
7
x
\frac{9 x^{2}}{4} \cdot \frac{3}{7 x}
4
9
x
2
⋅
7
x
3
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
1
2
x
2
⋅
5
x
2
7
\frac{1}{2 x^{2}} \cdot \frac{5 x^{2}}{7}
2
x
2
1
⋅
7
5
x
2
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
8
5
x
3
÷
6
x
7
\frac{8}{5 x^{3}} \div \frac{6 x}{7}
5
x
3
8
÷
7
6
x
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
7
2
x
2
÷
3
x
3
7
\frac{7}{2 x^{2}} \div \frac{3 x^{3}}{7}
2
x
2
7
÷
7
3
x
3
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
x
5
⋅
2
5
x
2
\frac{x}{5} \cdot \frac{2}{5 x^{2}}
5
x
⋅
5
x
2
2
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
x
5
⋅
3
x
3
5
\frac{x}{5} \cdot \frac{3 x^{3}}{5}
5
x
⋅
5
3
x
3
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
3
10
x
2
⋅
x
3
3
\frac{3}{10 x^{2}} \cdot \frac{x^{3}}{3}
10
x
2
3
⋅
3
x
3
\newline
Answer:
Get tutor help
Fully simplify the expression below and write your answer as a single fraction.
\newline
x
5
−
2
x
4
−
48
x
3
x
4
−
2
x
3
⋅
5
x
2
−
30
x
+
40
15
x
2
+
30
x
−
360
\frac{x^{5}-2 x^{4}-48 x^{3}}{x^{4}-2 x^{3}} \cdot \frac{5 x^{2}-30 x+40}{15 x^{2}+30 x-360}
x
4
−
2
x
3
x
5
−
2
x
4
−
48
x
3
⋅
15
x
2
+
30
x
−
360
5
x
2
−
30
x
+
40
\newline
Answer:
Get tutor help
Fully simplify the expression below and write your answer as a single fraction.
\newline
x
2
+
5
x
x
2
+
4
x
+
3
⋅
4
x
2
−
4
6
x
2
+
24
x
−
30
\frac{x^{2}+5 x}{x^{2}+4 x+3} \cdot \frac{4 x^{2}-4}{6 x^{2}+24 x-30}
x
2
+
4
x
+
3
x
2
+
5
x
⋅
6
x
2
+
24
x
−
30
4
x
2
−
4
\newline
Answer:
Get tutor help
Fully simplify the expression below and write your answer as a single fraction.
\newline
x
3
+
x
2
−
12
x
x
2
+
11
x
+
28
⋅
x
−
4
x
5
−
7
x
4
+
12
x
3
\frac{x^{3}+x^{2}-12 x}{x^{2}+11 x+28} \cdot \frac{x-4}{x^{5}-7 x^{4}+12 x^{3}}
x
2
+
11
x
+
28
x
3
+
x
2
−
12
x
⋅
x
5
−
7
x
4
+
12
x
3
x
−
4
\newline
Answer:
Get tutor help
Fully simplify the expression below and write your answer as a single fraction.
\newline
x
3
−
x
x
2
+
x
⋅
6
x
2
+
6
x
−
432
x
2
−
9
x
+
8
\frac{x^{3}-x}{x^{2}+x} \cdot \frac{6 x^{2}+6 x-432}{x^{2}-9 x+8}
x
2
+
x
x
3
−
x
⋅
x
2
−
9
x
+
8
6
x
2
+
6
x
−
432
\newline
Answer:
Get tutor help
Fully simplify the expression below and write your answer as a single fraction.
\newline
2
x
−
2
4
x
+
4
⋅
x
3
−
64
x
x
3
−
9
x
2
+
8
x
\frac{2 x-2}{4 x+4} \cdot \frac{x^{3}-64 x}{x^{3}-9 x^{2}+8 x}
4
x
+
4
2
x
−
2
⋅
x
3
−
9
x
2
+
8
x
x
3
−
64
x
\newline
Answer:
Get tutor help
Fully simplify the expression below and write your answer as a single fraction.
\newline
9
x
2
+
63
x
+
54
3
x
3
+
39
x
2
+
126
x
⋅
x
2
+
3
x
−
28
x
2
−
3
x
−
4
\frac{9 x^{2}+63 x+54}{3 x^{3}+39 x^{2}+126 x} \cdot \frac{x^{2}+3 x-28}{x^{2}-3 x-4}
3
x
3
+
39
x
2
+
126
x
9
x
2
+
63
x
+
54
⋅
x
2
−
3
x
−
4
x
2
+
3
x
−
28
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
2
−
4
x
2
+
7
x
⋅
x
2
−
49
x
2
−
9
x
+
14
\frac{x^{2}-4}{x^{2}+7 x} \cdot \frac{x^{2}-49}{x^{2}-9 x+14}
x
2
+
7
x
x
2
−
4
⋅
x
2
−
9
x
+
14
x
2
−
49
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
6
x
2
−
294
x
2
+
16
x
+
63
⋅
x
2
−
81
x
−
7
\frac{6 x^{2}-294}{x^{2}+16 x+63} \cdot \frac{x^{2}-81}{x-7}
x
2
+
16
x
+
63
6
x
2
−
294
⋅
x
−
7
x
2
−
81
\newline
Answer:
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\newline
11
9
−
11
6
\frac{11}{9}-\frac{11}{6}
9
11
−
6
11
\newline
Answer:
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