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Math Problems
Algebra 1
Multiplication with rational exponents
Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
8
−
1
3
log
8
27
w
3
)
\left(8^{-\frac{1}{3} \log _{8} 27 w^{3}}\right)
(
8
−
3
1
l
o
g
8
27
w
3
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
4
(
4
−
5
3
)
\log _{4}\left(4^{-\frac{5}{3}}\right)
lo
g
4
(
4
−
3
5
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
2
(
2
−
1
3
)
\log _{2}\left(2^{-\frac{1}{3}}\right)
lo
g
2
(
2
−
3
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
(
1
0
−
1
4
)
\log \left(10^{-\frac{1}{4}}\right)
lo
g
(
1
0
−
4
1
)
\newline
Answer:
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Find the
8
8
8
th term of the geometric sequence shown below.
\newline
−
7
x
,
−
7
x
6
,
−
7
x
11
,
…
-7 x,-7 x^{6},-7 x^{11}, \ldots
−
7
x
,
−
7
x
6
,
−
7
x
11
,
…
\newline
Answer:
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(
1
)
/
(
2
)
,
1
,
(
5
)
/
(
2
)
,
(
3
)
/
(
4
)
(1)/(2),1,(5)/(2),(3)/(4)
(
1
)
/
(
2
)
,
1
,
(
5
)
/
(
2
)
,
(
3
)
/
(
4
)
\newline
Find the range:
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5
1
3
⋅
x
−
1
=
1
2
9
5 \frac{1}{3} \cdot x-1=1 \frac{2}{9}
5
3
1
⋅
x
−
1
=
1
9
2
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(
13
0
)
+
(
13
1
)
+
(
13
2
)
+
(
13
3
)
+
(
13
4
)
+
(
13
5
)
+
(
13
6
)
\left(\begin{array}{c}13 \\ 0\end{array}\right)+\left(\begin{array}{c}13 \\ 1\end{array}\right)+\left(\begin{array}{c}13 \\ 2\end{array}\right)+\left(\begin{array}{c}13 \\ 3\end{array}\right)+\left(\begin{array}{c}13 \\ 4\end{array}\right)+\left(\begin{array}{c}13 \\ 5\end{array}\right)+\left(\begin{array}{c}13 \\ 6\end{array}\right)
(
13
0
)
+
(
13
1
)
+
(
13
2
)
+
(
13
3
)
+
(
13
4
)
+
(
13
5
)
+
(
13
6
)
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Simplify
(
6
x
3
4
y
−
2
4
x
−
1
4
y
−
3
)
−
1
⋅
(
2
x
3
y
2
x
y
1
2
)
2
\left(\frac{6 x^{\frac{3}{4}} y^{-2}}{4 x^{\frac{-1}{4}} y^{-3}}\right)^{-1} \cdot\left(\frac{2 x^{3} y}{2 x y^{\frac{1}{2}}}\right)^{2}
(
4
x
4
−
1
y
−
3
6
x
4
3
y
−
2
)
−
1
⋅
(
2
x
y
2
1
2
x
3
y
)
2
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5
log
2
x
+
3
log
2
z
5 \log _{2} x+3 \log _{2}z
5
lo
g
2
x
+
3
lo
g
2
z
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2
4
7
−
1
3
7
=
1
1
7
2 \frac{4}{7}-1 \frac{3}{7}=1 \frac{1}{7}
2
7
4
−
1
7
3
=
1
7
1
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Which correctly renames
7
8
\frac{7}{8}
8
7
and
5
6
\frac{5}{6}
6
5
using a common denominator?
\newline
A.
42
48
\frac{42}{48}
48
42
and
40
48
\frac{40}{48}
48
40
\newline
B.
42
48
\frac{42}{48}
48
42
and
30
48
\frac{30}{48}
48
30
\newline
C.
14
16
\frac{14}{16}
16
14
and
15
18
\frac{15}{18}
18
15
\newline
D.
28
24
\frac{28}{24}
24
28
and
20
24
\frac{20}{24}
24
20
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Click and drag like terms onto each other to simplify fully.
\newline
−
4
x
2
−
x
2
−
2
−
4
x
−
2
y
3
−
3
x
2
−
5
x
-4 x^{2}-x^{2}-2-4 x-2 y^{3}-3 x^{2}-5 x
−
4
x
2
−
x
2
−
2
−
4
x
−
2
y
3
−
3
x
2
−
5
x
Get tutor help
Fully simplify using only positive exponents.
\newline
2
x
6
y
3
2
x
6
y
5
\frac{2 x^{6} y^{3}}{2 x^{6} y^{5}}
2
x
6
y
5
2
x
6
y
3
\newline
Answer:
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Simplify:
\newline
(
−
2
m
4
)
(
5
m
3
)
\left(-2 m^{4}\right)\left(5 m^{3}\right)
(
−
2
m
4
)
(
5
m
3
)
\newline
Answer:
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Simplify:
\newline
(
−
7
k
)
(
2
k
3
)
(-7 k)\left(2 k^{3}\right)
(
−
7
k
)
(
2
k
3
)
\newline
Answer:
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Simplify the expression completely.
\newline
−
3
1
+
−
25
+
2
512
3
-3 \sqrt{1}+\sqrt{-25}+2 \sqrt[3]{512}
−
3
1
+
−
25
+
2
3
512
\newline
Answer:
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Simplify the expression completely.
\newline
−
−
100
−
2
4
+
216
3
-\sqrt{-100}-2 \sqrt{4}+\sqrt[3]{216}
−
−
100
−
2
4
+
3
216
\newline
Answer:
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Simplify the expression completely.
\newline
−
4
−
2
−
125
3
−
3
−
125
3
+
1
\sqrt{-4}-2 \sqrt[3]{-125}-3 \sqrt[3]{-125}+\sqrt{1}
−
4
−
2
3
−
125
−
3
3
−
125
+
1
\newline
Answer:
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Given the function
f
(
x
)
=
2
x
2
+
1
f(x)=2 x^{2}+1
f
(
x
)
=
2
x
2
+
1
, find the value of
f
(
−
5
2
)
f\left(-\frac{5}{2}\right)
f
(
−
2
5
)
in simplest form.
\newline
Answer:
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Given the function
f
(
x
)
=
2
x
2
−
3
x
3
f(x)=2 x^{2}-3 x^{3}
f
(
x
)
=
2
x
2
−
3
x
3
, find the value of
f
(
−
1
2
)
f\left(-\frac{1}{2}\right)
f
(
−
2
1
)
in simplest form.
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
2
x
+
1
f(x)=-\frac{1}{2} x+1
f
(
x
)
=
−
2
1
x
+
1
, find the value of
f
(
−
2
3
)
f\left(-\frac{2}{3}\right)
f
(
−
3
2
)
in simplest form.
\newline
Answer:
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Given the function
f
(
x
)
=
−
2
x
3
+
7
4
x
f(x)=-2 x^{3}+\frac{7}{4} x
f
(
x
)
=
−
2
x
3
+
4
7
x
, find the value of
f
(
3
2
)
f\left(\frac{3}{2}\right)
f
(
2
3
)
in simplest form.
\newline
Answer:
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Simplify the expression completely.
\newline
5
1
+
−
1000
3
+
2
8
3
5 \sqrt{1}+\sqrt[3]{-1000}+2 \sqrt[3]{8}
5
1
+
3
−
1000
+
2
3
8
\newline
Answer:
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Simplify the expression completely.
\newline
−
1
3
+
2
−
25
−
2
−
1000
3
-\sqrt[3]{1}+2 \sqrt{-25}-2 \sqrt[3]{-1000}
−
3
1
+
2
−
25
−
2
3
−
1000
\newline
Answer:
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Solve for
x
x
x
.
\newline
1
4
−
4
x
=
3
4
x
\frac{1}{4}-\frac{4}{x}=\frac{3}{4 x}
4
1
−
x
4
=
4
x
3
\newline
Answer:
x
=
x=
x
=
Get tutor help
Simplify the following expression completely.
\newline
x
2
−
8
x
+
15
x
2
+
3
x
−
40
\frac{x^{2}-8 x+15}{x^{2}+3 x-40}
x
2
+
3
x
−
40
x
2
−
8
x
+
15
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
13
x
+
40
x
2
+
4
x
−
45
\frac{x^{2}-13 x+40}{x^{2}+4 x-45}
x
2
+
4
x
−
45
x
2
−
13
x
+
40
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
4
x
−
60
x
2
−
2
x
−
24
\frac{x^{2}+4 x-60}{x^{2}-2 x-24}
x
2
−
2
x
−
24
x
2
+
4
x
−
60
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
4
−
8
x
3
x
2
−
5
x
−
24
\frac{x^{4}-8 x^{3}}{x^{2}-5 x-24}
x
2
−
5
x
−
24
x
4
−
8
x
3
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
+
16
x
+
63
x
2
−
81
\frac{x^{2}+16 x+63}{x^{2}-81}
x
2
−
81
x
2
+
16
x
+
63
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
3
x
−
28
x
2
+
6
x
+
8
\frac{x^{2}-3 x-28}{x^{2}+6 x+8}
x
2
+
6
x
+
8
x
2
−
3
x
−
28
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
2
x
−
15
x
2
−
9
\frac{x^{2}-2 x-15}{x^{2}-9}
x
2
−
9
x
2
−
2
x
−
15
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
6
x
−
16
x
2
−
2
x
−
48
\frac{x^{2}-6 x-16}{x^{2}-2 x-48}
x
2
−
2
x
−
48
x
2
−
6
x
−
16
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
4
x
2
+
3
x
+
2
\frac{x^{2}-4}{x^{2}+3 x+2}
x
2
+
3
x
+
2
x
2
−
4
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
4
x
−
5
x
2
−
4
x
−
45
\frac{x^{2}+4 x-5}{x^{2}-4 x-45}
x
2
−
4
x
−
45
x
2
+
4
x
−
5
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
x
−
42
x
2
−
12
x
+
35
\frac{x^{2}-x-42}{x^{2}-12 x+35}
x
2
−
12
x
+
35
x
2
−
x
−
42
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
16
x
+
63
x
2
+
3
x
−
70
\frac{x^{2}-16 x+63}{x^{2}+3 x-70}
x
2
+
3
x
−
70
x
2
−
16
x
+
63
\newline
Answer:
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Simplify the expression completely if possible.
\newline
8
x
2
x
4
+
8
x
3
\frac{8 x^{2}}{x^{4}+8 x^{3}}
x
4
+
8
x
3
8
x
2
\newline
Answer:
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Simplify the expression completely if possible.
\newline
4
x
2
−
4
x
x
2
−
8
x
+
7
\frac{4 x^{2}-4 x}{x^{2}-8 x+7}
x
2
−
8
x
+
7
4
x
2
−
4
x
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
16
x
2
+
5
x
+
4
\frac{x^{2}-16}{x^{2}+5 x+4}
x
2
+
5
x
+
4
x
2
−
16
\newline
Answer:
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Simplify the expression completely if possible.
\newline
3
x
2
x
2
−
3
x
\frac{3 x^{2}}{x^{2}-3 x}
x
2
−
3
x
3
x
2
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
5
x
x
2
−
25
\frac{x^{2}-5 x}{x^{2}-25}
x
2
−
25
x
2
−
5
x
\newline
Answer:
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For the function
f
(
x
)
=
7
−
4
x
3
x
+
8
f(x)=\frac{7-4 x}{3 x+8}
f
(
x
)
=
3
x
+
8
7
−
4
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
1
7
+
2
x
f(x)=\frac{1}{7+2 x}
f
(
x
)
=
7
+
2
x
1
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
5
3
x
+
4
f(x)=\frac{5}{3 x+4}
f
(
x
)
=
3
x
+
4
5
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
3
x
5
x
−
4
f(x)=\frac{3 x}{5 x-4}
f
(
x
)
=
5
x
−
4
3
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
3
x
5
x
−
3
f(x)=\frac{3 x}{5 x-3}
f
(
x
)
=
5
x
−
3
3
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
−
3
1
+
3
x
f(x)=\frac{-3}{1+3 x}
f
(
x
)
=
1
+
3
x
−
3
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
For the function
f
(
x
)
=
3
x
3
x
+
8
f(x)=\frac{3 x}{3 x+8}
f
(
x
)
=
3
x
+
8
3
x
, find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
\newline
Answer:
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
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