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Math Problems
Algebra 1
Simplify expressions involving rational exponents
Simplify. Assume all variables are positive.
\newline
w
1
2
w
3
2
\frac{w^{\frac{1}{2}}}{w^{\frac{3}{2}}}
w
2
3
w
2
1
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
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Simplify. Assume all variables are positive.
\newline
v
7
3
v
8
3
\frac{v^{\frac{7}{3}}}{v^{\frac{8}{3}}}
v
3
8
v
3
7
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
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Simplify. Assume all variables are positive.
\newline
b
9
4
b
5
4
\frac{b^{\frac{9}{4}}}{b^{\frac{5}{4}}}
b
4
5
b
4
9
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
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Simplify. Assume all variables are positive.
\newline
r
3
2
r
5
2
\frac{r^{\frac{3}{2}}}{r^{\frac{5}{2}}}
r
2
5
r
2
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
s
5
4
s
7
4
\frac{s^{\frac{5}{4}}}{s^{\frac{7}{4}}}
s
4
7
s
4
5
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
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Simplify. Assume all variables are positive.
\newline
w
9
4
w
11
4
\frac{w^{\frac{9}{4}}}{w^{\frac{11}{4}}}
w
4
11
w
4
9
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
w
3
4
w
11
4
\frac{w^{\frac{3}{4}}}{w^{\frac{11}{4}}}
w
4
11
w
4
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
w
8
3
w
2
3
\frac{w^{\frac{8}{3}}}{w^{\frac{2}{3}}}
w
3
2
w
3
8
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
u
4
3
u
5
3
\frac{u^{\frac{4}{3}}}{u^{\frac{5}{3}}}
u
3
5
u
3
4
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
b
8
3
b
1
3
\frac{b^{\frac{8}{3}}}{b^{\frac{1}{3}}}
b
3
1
b
3
8
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
u
3
2
u
5
2
\frac{u^{\frac{3}{2}}}{u^{\frac{5}{2}}}
u
2
5
u
2
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
r
3
4
r
9
4
\frac{r^{\frac{3}{4}}}{r^{\frac{9}{4}}}
r
4
9
r
4
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
v
4
3
v
2
3
\frac{v^{\frac{4}{3}}}{v^{\frac{2}{3}}}
v
3
2
v
3
4
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
r
11
4
r
9
4
\frac{r^{\frac{11}{4}}}{r^{\frac{9}{4}}}
r
4
9
r
4
11
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
w
3
2
w
5
2
\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}
w
2
5
w
2
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
z
8
5
z
13
5
\frac{z^{\frac{8}{5}}}{z^{\frac{13}{5}}}
z
5
13
z
5
8
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
z
6
5
z
13
5
\frac{z^{\frac{6}{5}}}{z^{\frac{13}{5}}}
z
5
13
z
5
6
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
s
3
4
s
1
4
\frac{s^{\frac{3}{4}}}{s^{\frac{1}{4}}}
s
4
1
s
4
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
b
3
2
b
1
2
\frac{b^{\frac{3}{2}}}{b^{\frac{1}{2}}}
b
2
1
b
2
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
d
1
3
d
4
3
\frac{d^{\frac{1}{3}}}{d^{\frac{4}{3}}}
d
3
4
d
3
1
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
s
4
3
s
8
3
\frac{s^{\frac{4}{3}}}{s^{\frac{8}{3}}}
s
3
8
s
3
4
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
z
3
4
z
1
4
\frac{z^{\frac{3}{4}}}{z^{\frac{1}{4}}}
z
4
1
z
4
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
s
7
3
s
4
3
\frac{s^{\frac{7}{3}}}{s^{\frac{4}{3}}}
s
3
4
s
3
7
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
u
3
4
u
7
4
\frac{u^{\frac{3}{4}}}{u^{\frac{7}{4}}}
u
4
7
u
4
3
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
w
1
3
w
4
3
\frac{w^{\frac{1}{3}}}{w^{\frac{4}{3}}}
w
3
4
w
3
1
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
Get tutor help
Boats
A
A
A
and
B
B
B
are participating in a race. Their velocities are represented by vectors
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
, respectively.
\newline
Which option best describes the meaning of the following statement?
\newline
a
⃗
=
b
⃗
\vec{a}=\vec{b}
a
=
b
\newline
Choose
1
1
1
answer:
\newline
(A) The two boats move at the same speed and in the same direction.
\newline
(B) The two boats move at the same speed, but not necessarily in the same direction.
\newline
(C) The two boats move in the same direction, but not necessarily at the same speed.
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Simplify. Assume all variables are positive.
\newline
v
7
4
⋅
v
9
4
v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}
v
4
7
⋅
v
4
9
\newline
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
\newline
Get tutor help
