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Math Problems
Algebra 2
Simplify expressions involving rational exponents I
8
8
8
. The following matrix consists of a shoe store's inventory of sneakers, slippers and garden boots in sizes small, medium, and large:
\newline
\begin{tabular}{|l|l|l|l|}
\newline
\hline & Small & Medium & Large \\
\newline
\hline Sneakers &
20
20
20
&
15
15
15
&
10
10
10
\\
\newline
\hline Slippers &
30
30
30
&
25
25
25
&
18
18
18
\\
\newline
\hline Garden Boots &
15
15
15
&
12
12
12
&
8
8
8
\\
\newline
\hline
\newline
\end{tabular}
\newline
(a) Form a
3
3
3
x
3
3
3
matrix to represent the information given above.
\newline
Sneakers sell for
$
150
\$ 150
$150
; Slippers sell for
$
30
\$ 30
$30
, and Garden Boots sell for
$
125
\$ 125
$125
.
\newline
(b) Form a
1
1
1
x
3
3
3
matrix to represent this information.
\newline
[
2
]
[2]
[
2
]
\newline
(c) Use matrix multiplication to determine how much the inventory is worth.
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Simplify. Assume all variables are positive.
\newline
z
1
4
z
7
4
\frac{z^{\frac{1}{4}}}{z^{\frac{7}{4}}}
z
4
7
z
4
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
1
3
s
5
3
\frac{s^{\frac{1}{3}}}{s^{\frac{5}{3}}}
s
3
5
s
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
w
1
4
w
7
4
\frac{w^{\frac{1}{4}}}{w^{\frac{7}{4}}}
w
4
7
w
4
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
b
6
5
b
7
5
\frac{b^{\frac{6}{5}}}{b^{\frac{7}{5}}}
b
5
7
b
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
u
1
3
⋅
u
1
3
u^{\frac{1}{3}} \cdot u^{\frac{1}{3}}
u
3
1
⋅
u
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
b
7
5
b
9
5
\frac{b^{\frac{7}{5}}}{b^{\frac{9}{5}}}
b
5
9
b
5
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
b
6
5
×
b
7
5
b^{\frac{6}{5}} \times b^{\frac{7}{5}}
b
5
6
×
b
5
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
v
7
3
⋅
v
8
3
v^{\frac{7}{3}} \cdot v^{\frac{8}{3}}
v
3
7
⋅
v
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
w
13
7
w
12
7
\frac{w^{\frac{13}{7}}}{w^{\frac{12}{7}}}
w
7
12
w
7
13
\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
7
3
u^{\frac{4}{3}} \times u^{\frac{7}{3}}
u
3
4
×
u
3
7
\newline
Write your answer in the form
A
A
A
or
A
/
B
A/B
A
/
B
, 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
y
3
2
⋅
y
3
2
y^{\frac{3}{2}} \cdot y^{\frac{3}{2}}
y
2
3
⋅
y
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
u
5
2
×
u
3
2
u^{\frac{5}{2}} \times u^{\frac{3}{2}}
u
2
5
×
u
2
3
\newline
Write your answer in the form
A
A
A
or
A
/
B
A/B
A
/
B
, 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
17
6
z
7
6
\frac{z^{\frac{17}{6}}}{z^{\frac{7}{6}}}
z
6
7
z
6
17
\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
13
6
z
5
6
\frac{z^{\frac{13}{6}}}{z^{\frac{5}{6}}}
z
6
5
z
6
13
\newline
Write your answer in the form
A
A
A
or
A
/
B
A/B
A
/
B
, 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
4
3
×
w
7
3
w^{\frac{4}{3}} \times w^{\frac{7}{3}}
w
3
4
×
w
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
______
\newline
Get tutor help
Simplify. Assume all variables are positive.
\newline
d
6
5
d
2
5
\frac{d^{\frac{6}{5}}}{d^{\frac{2}{5}}}
d
5
2
d
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
y
3
2
×
y
5
2
y^{\frac{3}{2}} \times y^{\frac{5}{2}}
y
2
3
×
y
2
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
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
u
11
4
u
11
4
⋅
u
5
4
\frac{u^{\frac{11}{4}}}{u^{\frac{11}{4}} \cdot u^{\frac{5}{4}}}
u
4
11
⋅
u
4
5
u
4
11
\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
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
x
1
4
x
11
4
\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}
x
4
11
x
4
1
\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
