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Math Problems
Precalculus
Operations with rational exponents
792
7
=
4
3
×
22
7
×
r
3
\frac{792}{7}=\frac{4}{3} \times \frac{22}{7} \times r^{3}
7
792
=
3
4
×
7
22
×
r
3
.
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35
x
12
y
4
z
7
7
x
6
y
8
z
6
\frac{35 x^{12} y^{4} z^{7}}{7 x^{6} y^{8} z^{6}}
7
x
6
y
8
z
6
35
x
12
y
4
z
7
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12
g
3
v
4
×
4
g
2
v
7
12 g^{3} v^{4} \times 4 g^{2} v^{7}
12
g
3
v
4
×
4
g
2
v
7
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18
x
7
y
4
12
x
9
y
4
\frac{18 x^{7} y^{4}}{12 x^{9} y^{4}}
12
x
9
y
4
18
x
7
y
4
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8
3
⋅
8
−
5
⋅
8
y
=
8
−
2
=
1
8
2
8^{3} \cdot 8^{-5} \cdot 8^{y}=8^{-2}=\frac{1}{8^{2}}
8
3
⋅
8
−
5
⋅
8
y
=
8
−
2
=
8
2
1
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Simplify:
4
3
−
1
2
n
=
5
8
\frac{4}{3}-\frac{1}{2} n=\frac{5}{8}
3
4
−
2
1
n
=
8
5
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3
3
3
.
(
16
÷
4
)
+
(
10
−
3
)
(16 \div 4)+(10-3)
(
16
÷
4
)
+
(
10
−
3
)
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(iii)
−
2
5
×
(
3
8
−
25
)
\frac{-2}{5} \times\left(\frac{3}{8}-25\right)
5
−
2
×
(
8
3
−
25
)
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Write the expression as a single power of
x
x
x
.
\newline
x
4
3
x
2
3
\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}
x
3
2
x
3
4
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Integrate
\newline
ln
(
5
12
a
)
da
\ln \left(\frac{5}{12} a\right) \text { da }
ln
(
12
5
a
)
da
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If
8
5
6
−
8
1
2
=
8
m
8^{\frac{5}{6}}-8^{\frac{1}{2}}=8^{m}
8
6
5
−
8
2
1
=
8
m
for some value of
m
m
m
, what is the value of
m
m
m
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
\frac{1}{3}
3
1
\newline
(B)
1
2
\frac{1}{2}
2
1
\newline
(C)
1
1
1
\newline
(D)
5
3
\frac{5}{3}
3
5
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(
2
3
)
4
⋅
(
2
34
)
(
2
5
)
8
\frac{\left(2^{3}\right)^{4} \cdot\left(2^{34}\right)}{\left(2^{5}\right)^{8}}
(
2
5
)
8
(
2
3
)
4
⋅
(
2
34
)
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Write the answer in proper scientific notation:
\newline
2
8
x
1
0
−
5
\frac{2}{8x10^{-5}}
8
x
1
0
−
5
2
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11
10
÷
5
3
=
\frac{11}{10} \div \frac{5}{3}=
10
11
÷
3
5
=
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5
9
5
x
=
625
\frac{5^{9}}{5^{x}}=625
5
x
5
9
=
625
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3
7
=
15
x
\frac{3}{7}=\frac{15}{x}
7
3
=
x
15
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24
x
5
z
2
12
x
7
z
\frac{24 x^{5} z^{2}}{12 x^{7} z}
12
x
7
z
24
x
5
z
2
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(
2
5
+
3
10
)
÷
7
15
\left(\frac{2}{5}+\frac{3}{10}\right) \div \frac{7}{15}
(
5
2
+
10
3
)
÷
15
7
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Jordan has an extension ladder that currently reaches a height of
11
3
5
11 \frac{3}{5}
11
5
3
feet. She needs the ladder to extend to a height of
15
1
5
15 \frac{1}{5}
15
5
1
feet. How much longer, in feet, does the ladder need to be extended?
\newline
(A)
3
3
5
3 \frac{3}{5}
3
5
3
\newline
(B)
4
2
5
4 \frac{2}{5}
4
5
2
\newline
(C)
11
4
5
11 \frac{4}{5}
11
5
4
\newline
(D)
26
4
5
26 \frac{4}{5}
26
5
4
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2
x
3
+
32
x
2
+
128
x
2 x^{3}+32 x^{2}+128 x
2
x
3
+
32
x
2
+
128
x
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Perform the following operation and express in simplest form.
\newline
x
2
−
12
x
+
35
x
2
−
25
÷
3
x
−
21
8
x
+
40
\frac{x^{2}-12 x+35}{x^{2}-25} \div \frac{3 x-21}{8 x+40}
x
2
−
25
x
2
−
12
x
+
35
÷
8
x
+
40
3
x
−
21
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
+
9
x
x
−
9
÷
x
2
−
81
x
2
−
7
x
−
18
\frac{x^{2}+9 x}{x-9} \div \frac{x^{2}-81}{x^{2}-7 x-18}
x
−
9
x
2
+
9
x
÷
x
2
−
7
x
−
18
x
2
−
81
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
−
81
x
2
+
7
x
−
18
÷
x
−
9
9
x
2
\frac{x^{2}-81}{x^{2}+7 x-18} \div \frac{x-9}{9 x^{2}}
x
2
+
7
x
−
18
x
2
−
81
÷
9
x
2
x
−
9
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
+
4
x
−
45
3
x
2
÷
x
2
+
6
x
−
27
5
x
\frac{x^{2}+4 x-45}{3 x^{2}} \div \frac{x^{2}+6 x-27}{5 x}
3
x
2
x
2
+
4
x
−
45
÷
5
x
x
2
+
6
x
−
27
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
6
x
+
12
x
2
+
11
x
+
18
÷
x
+
4
x
2
+
6
x
−
27
\frac{6 x+12}{x^{2}+11 x+18} \div \frac{x+4}{x^{2}+6 x-27}
x
2
+
11
x
+
18
6
x
+
12
÷
x
2
+
6
x
−
27
x
+
4
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
2
+
11
x
+
24
x
2
−
9
÷
4
x
+
32
x
3
\frac{x^{2}+11 x+24}{x^{2}-9} \div \frac{4 x+32}{x^{3}}
x
2
−
9
x
2
+
11
x
+
24
÷
x
3
4
x
+
32
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
+
6
x
−
9
÷
x
2
−
3
x
−
54
x
2
−
18
x
+
81
\frac{x+6}{x-9} \div \frac{x^{2}-3 x-54}{x^{2}-18 x+81}
x
−
9
x
+
6
÷
x
2
−
18
x
+
81
x
2
−
3
x
−
54
\newline
Answer:
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Perform the following operation and express in simplest form.
\newline
x
4
−
6
x
3
x
2
−
14
x
+
48
÷
x
x
2
−
64
\frac{x^{4}-6 x^{3}}{x^{2}-14 x+48} \div \frac{x}{x^{2}-64}
x
2
−
14
x
+
48
x
4
−
6
x
3
÷
x
2
−
64
x
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
3
x
5
−
75
x
3
x
4
+
5
x
3
⋅
x
2
+
10
x
+
21
x
2
−
2
x
−
15
\frac{3 x^{5}-75 x^{3}}{x^{4}+5 x^{3}} \cdot \frac{x^{2}+10 x+21}{x^{2}-2 x-15}
x
4
+
5
x
3
3
x
5
−
75
x
3
⋅
x
2
−
2
x
−
15
x
2
+
10
x
+
21
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
10
x
2
−
10
x
−
420
5
x
2
−
80
x
+
315
⋅
x
3
−
14
x
2
+
45
x
x
4
−
5
x
3
\frac{10 x^{2}-10 x-420}{5 x^{2}-80 x+315} \cdot \frac{x^{3}-14 x^{2}+45 x}{x^{4}-5 x^{3}}
5
x
2
−
80
x
+
315
10
x
2
−
10
x
−
420
⋅
x
4
−
5
x
3
x
3
−
14
x
2
+
45
x
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
1
6
x
3
⋅
4
5
x
2
\frac{1}{6 x^{3}} \cdot \frac{4}{5 x^{2}}
6
x
3
1
⋅
5
x
2
4
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
9
7
x
2
5
x
3
2
\frac{\frac{9}{7 x^{2}}}{\frac{5 x^{3}}{2}}
2
5
x
3
7
x
2
9
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
5
x
2
4
7
10
x
2
\frac{\frac{5 x^{2}}{4}}{\frac{7}{10 x^{2}}}
10
x
2
7
4
5
x
2
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
5
2
x
3
3
x
7
\frac{\frac{5}{2 x^{3}}}{\frac{3 x}{7}}
7
3
x
2
x
3
5
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
8
7
x
2
÷
2
3
x
3
\frac{8}{7 x^{2}} \div \frac{2}{3 x^{3}}
7
x
2
8
÷
3
x
3
2
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
2
x
3
5
3
x
3
4
\frac{\frac{2 x^{3}}{5}}{\frac{3 x^{3}}{4}}
4
3
x
3
5
2
x
3
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
9
7
x
3
⋅
3
2
x
3
\frac{9}{7 x^{3}} \cdot \frac{3}{2 x^{3}}
7
x
3
9
⋅
2
x
3
3
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
10
9
x
3
÷
5
7
x
2
\frac{10}{9 x^{3}} \div \frac{5}{7 x^{2}}
9
x
3
10
÷
7
x
2
5
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
4
−
25
x
2
x
2
+
8
x
+
15
⋅
x
2
+
2
x
−
3
6
x
3
−
36
x
2
+
30
x
\frac{x^{4}-25 x^{2}}{x^{2}+8 x+15} \cdot \frac{x^{2}+2 x-3}{6 x^{3}-36 x^{2}+30 x}
x
2
+
8
x
+
15
x
4
−
25
x
2
⋅
6
x
3
−
36
x
2
+
30
x
x
2
+
2
x
−
3
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
4
x
5
−
28
x
4
−
32
x
3
2
x
5
−
10
x
4
−
12
x
3
⋅
x
−
6
x
2
−
13
x
+
40
\frac{4 x^{5}-28 x^{4}-32 x^{3}}{2 x^{5}-10 x^{4}-12 x^{3}} \cdot \frac{x-6}{x^{2}-13 x+40}
2
x
5
−
10
x
4
−
12
x
3
4
x
5
−
28
x
4
−
32
x
3
⋅
x
2
−
13
x
+
40
x
−
6
\newline
Answer:
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Perform the operation and simplify the answer fully.
\newline
1
8
x
3
⋅
5
x
4
\frac{1}{8 x^{3}} \cdot \frac{5 x}{4}
8
x
3
1
⋅
4
5
x
\newline
Answer:
Get tutor help
Fully simplify the expression below and write your answer as a single fraction.
\newline
x
3
−
6
x
2
−
7
x
3
x
+
27
⋅
x
2
−
81
x
5
−
8
x
4
−
9
x
3
\frac{x^{3}-6 x^{2}-7 x}{3 x+27} \cdot \frac{x^{2}-81}{x^{5}-8 x^{4}-9 x^{3}}
3
x
+
27
x
3
−
6
x
2
−
7
x
⋅
x
5
−
8
x
4
−
9
x
3
x
2
−
81
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
3
−
6
x
2
−
7
x
4
x
2
−
64
x
+
252
⋅
x
−
9
x
+
3
\frac{x^{3}-6 x^{2}-7 x}{4 x^{2}-64 x+252} \cdot \frac{x-9}{x+3}
4
x
2
−
64
x
+
252
x
3
−
6
x
2
−
7
x
⋅
x
+
3
x
−
9
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
2
x
2
−
14
x
x
5
−
6
x
4
−
7
x
3
⋅
x
2
−
9
x
−
10
x
2
−
16
x
+
60
\frac{2 x^{2}-14 x}{x^{5}-6 x^{4}-7 x^{3}} \cdot \frac{x^{2}-9 x-10}{x^{2}-16 x+60}
x
5
−
6
x
4
−
7
x
3
2
x
2
−
14
x
⋅
x
2
−
16
x
+
60
x
2
−
9
x
−
10
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
+
6
x
5
−
4
x
4
−
60
x
3
⋅
5
x
5
−
5
x
4
−
450
x
3
x
2
+
12
x
+
27
\frac{x+6}{x^{5}-4 x^{4}-60 x^{3}} \cdot \frac{5 x^{5}-5 x^{4}-450 x^{3}}{x^{2}+12 x+27}
x
5
−
4
x
4
−
60
x
3
x
+
6
⋅
x
2
+
12
x
+
27
5
x
5
−
5
x
4
−
450
x
3
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
+
6
x
2
+
9
x
+
18
⋅
x
3
−
x
2
−
12
x
x
3
−
11
x
2
+
28
x
\frac{x+6}{x^{2}+9 x+18} \cdot \frac{x^{3}-x^{2}-12 x}{x^{3}-11 x^{2}+28 x}
x
2
+
9
x
+
18
x
+
6
⋅
x
3
−
11
x
2
+
28
x
x
3
−
x
2
−
12
x
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
3
−
25
x
x
2
+
12
x
+
35
⋅
x
+
7
x
4
+
9
x
3
\frac{x^{3}-25 x}{x^{2}+12 x+35} \cdot \frac{x+7}{x^{4}+9 x^{3}}
x
2
+
12
x
+
35
x
3
−
25
x
⋅
x
4
+
9
x
3
x
+
7
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
3
x
+
3
9
x
2
+
81
x
+
72
⋅
x
2
−
64
x
2
−
2
x
−
48
\frac{3 x+3}{9 x^{2}+81 x+72} \cdot \frac{x^{2}-64}{x^{2}-2 x-48}
9
x
2
+
81
x
+
72
3
x
+
3
⋅
x
2
−
2
x
−
48
x
2
−
64
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
x
−
2
10
x
2
−
60
x
+
80
⋅
x
2
−
10
x
+
24
x
5
−
9
x
4
+
18
x
3
\frac{x-2}{10 x^{2}-60 x+80} \cdot \frac{x^{2}-10 x+24}{x^{5}-9 x^{4}+18 x^{3}}
10
x
2
−
60
x
+
80
x
−
2
⋅
x
5
−
9
x
4
+
18
x
3
x
2
−
10
x
+
24
\newline
Answer:
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Fully simplify the expression below and write your answer as a single fraction.
\newline
2
x
4
−
8
x
2
x
4
−
10
x
3
⋅
x
+
7
4
x
2
+
36
x
+
56
\frac{2 x^{4}-8 x^{2}}{x^{4}-10 x^{3}} \cdot \frac{x+7}{4 x^{2}+36 x+56}
x
4
−
10
x
3
2
x
4
−
8
x
2
⋅
4
x
2
+
36
x
+
56
x
+
7
\newline
Answer:
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