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Math Problems
Precalculus
Simplify expressions involving rational exponents
The thickness of a strand of cotton is about
9
×
1
0
−
1
9 \times 10^{-1}
9
×
1
0
−
1
millimeters. The thickness of a strand of silk is about
3
×
1
0
−
2
3 \times 10^{-2}
3
×
1
0
−
2
millimeters.
\newline
Use these numbers to complete the sentence below. Write your answer in standard form, without using exponents.
\newline
A strand of cotton is about ____ times as thick as a strand of silk.
Get tutor help
Simplify. Assume all variables are positive.
\newline
b
7
4
b
3
4
⋅
b
7
4
\frac{b^{\frac{7}{4}}}{b^{\frac{3}{4}} \cdot b^{\frac{7}{4}}}
b
4
3
⋅
b
4
7
b
4
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
x
2
3
x
5
3
⋅
x
1
3
\frac{x^{\frac{2}{3}}}{x^{\frac{5}{3}} \cdot x^{\frac{1}{3}}}
x
3
5
⋅
x
3
1
x
3
2
\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
7
3
⋅
u
4
3
\frac{u^{\frac{1}{3}}}{u^{\frac{7}{3}} \cdot u^{\frac{4}{3}}}
u
3
7
⋅
u
3
4
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
d
5
4
d
5
4
⋅
d
7
4
\frac{d^{\frac{5}{4}}}{d^{\frac{5}{4}} \cdot d^{\frac{7}{4}}}
d
4
5
⋅
d
4
7
d
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
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
x
1
/
4
x
3
/
4
⋅
x
9
/
4
\frac{x^{1/4}}{x^{3/4} \cdot x^{9/4}}
x
3/4
⋅
x
9/4
x
1/4
\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
s
3
2
s
5
2
⋅
s
1
2
\frac{s^{\frac{3}{2}}}{s^{\frac{5}{2}} \cdot s^{\frac{1}{2}}}
s
2
5
⋅
s
2
1
s
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
______
\newline
Get tutor help
Simplify. Assume all variables are positive.
\newline
u
1
2
u
5
2
⋅
u
1
2
\frac{u^{\frac{1}{2}}}{u^{\frac{5}{2}} \cdot u^{\frac{1}{2}}}
u
2
5
⋅
u
2
1
u
2
1
\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
d
5
4
d
9
4
⋅
d
5
4
\frac{d^{\frac{5}{4}}}{d^{\frac{9}{4}} \cdot d^{\frac{5}{4}}}
d
4
9
⋅
d
4
5
d
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
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
u
4
3
u
7
3
⋅
u
4
3
\frac{u^{\frac{4}{3}}}{u^{\frac{7}{3}} \cdot u^{\frac{4}{3}}}
u
3
7
⋅
u
3
4
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
x
1
/
4
x
3
/
4
⋅
x
7
/
4
\frac{x^{1/4}}{x^{3/4} \cdot x^{7/4}}
x
3/4
⋅
x
7/4
x
1/4
\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
1
3
w
8
3
⋅
w
5
3
\frac{w^{\frac{1}{3}}}{w^{\frac{8}{3}} \cdot w^{\frac{5}{3}}}
w
3
8
⋅
w
3
5
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
Simplify. Assume all variables are positive.
\newline
u
9
4
u
11
4
⋅
u
9
4
\frac{u^{\frac{9}{4}}}{u^{\frac{11}{4}} \cdot u^{\frac{9}{4}}}
u
4
11
⋅
u
4
9
u
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
d
3
4
d
5
4
⋅
d
9
4
\frac{d^{\frac{3}{4}}}{d^{\frac{5}{4}} \cdot d^{\frac{9}{4}}}
d
4
5
⋅
d
4
9
d
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
r
3
4
r
9
4
⋅
r
3
4
\frac{r^{\frac{3}{4}}}{r^{\frac{9}{4}} \cdot r^{\frac{3}{4}}}
r
4
9
⋅
r
4
3
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
x
1
/
2
x
5
/
2
⋅
x
3
/
2
\frac{x^{1/2}}{x^{5/2} \cdot x^{3/2}}
x
5/2
⋅
x
3/2
x
1/2
\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
c
3
2
c
5
2
⋅
c
1
2
\frac{c^{\frac{3}{2}}}{c^{\frac{5}{2}} \cdot c^{\frac{1}{2}}}
c
2
5
⋅
c
2
1
c
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
3
4
z
9
4
⋅
z
3
4
\frac{z^{\frac{3}{4}}}{z^{\frac{9}{4}} \cdot z^{\frac{3}{4}}}
z
4
9
⋅
z
4
3
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
v
2
3
v
7
3
⋅
v
5
3
\frac{v^{\frac{2}{3}}}{v^{\frac{7}{3}} \cdot v^{\frac{5}{3}}}
v
3
7
⋅
v
3
5
v
3
2
\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
t
3
2
t
5
2
⋅
t
3
2
\frac{t^{\frac{3}{2}}}{t^{\frac{5}{2}} \cdot t^{\frac{3}{2}}}
t
2
5
⋅
t
2
3
t
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
3
4
s
9
4
⋅
s
1
4
\frac{s^{\frac{3}{4}}}{s^{\frac{9}{4}} \cdot s^{\frac{1}{4}}}
s
4
9
⋅
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
r
4
3
⋅
r
7
3
r
5
3
\frac{r^{\frac{4}{3}} \cdot r^{\frac{7}{3}}}{r^{\frac{5}{3}}}
r
3
5
r
3
4
⋅
r
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
2
u
3
2
⋅
u
1
2
\frac{u^{\frac{3}{2}}}{u^{\frac{3}{2}} \cdot u^{\frac{1}{2}}}
u
2
3
⋅
u
2
1
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
b
3
2
b
5
2
\frac{b^{\frac{3}{2}}}{b^{\frac{5}{2}}}
b
2
5
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
b
7
4
b
3
4
\frac{b^{\frac{7}{4}}}{b^{\frac{3}{4}}}
b
4
3
b
4
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
2
3
b
4
3
\frac{b^{\frac{2}{3}}}{b^{\frac{4}{3}}}
b
3
4
b
3
2
\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
2
3
x
8
3
\frac{x^{\frac{2}{3}}}{x^{\frac{8}{3}}}
x
3
8
x
3
2
\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
1
2
⋅
b
3
2
b^{\frac{1}{2}} \cdot b^{\frac{3}{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
x
7
3
×
x
8
3
x^{\frac{7}{3}} \times x^{\frac{8}{3}}
x
3
7
×
x
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
c
13
6
⋅
c
13
6
c^{\frac{13}{6}} \cdot c^{\frac{13}{6}}
c
6
13
⋅
c
6
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
r
3
2
⋅
r
3
2
r^{\frac{3}{2}} \cdot r^{\frac{3}{2}}
r
2
3
⋅
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
u
3
2
⋅
u
5
2
u^{\frac{3}{2}} \cdot u^{\frac{5}{2}}
u
2
3
⋅
u
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
s
1
3
⋅
s
8
3
s^{\frac{1}{3}} \cdot s^{\frac{8}{3}}
s
3
1
⋅
s
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
d
4
3
⋅
d
1
3
d^{\frac{4}{3}} \cdot d^{\frac{1}{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
t
8
5
⋅
t
11
5
t^{\frac{8}{5}} \cdot t^{\frac{11}{5}}
t
5
8
⋅
t
5
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
x
3
5
×
x
13
5
x^{\frac{3}{5}} \times x^{\frac{13}{5}}
x
5
3
×
x
5
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
z
5
7
⋅
z
12
7
z^{\frac{5}{7}} \cdot z^{\frac{12}{7}}
z
7
5
⋅
z
7
12
\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
8
7
⋅
s
13
7
s^{\frac{8}{7}} \cdot s^{\frac{13}{7}}
s
7
8
⋅
s
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
t
7
6
⋅
t
17
6
t^{\frac{7}{6}} \cdot t^{\frac{17}{6}}
t
6
7
⋅
t
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
s
5
7
⋅
s
1
7
s^{\frac{5}{7}} \cdot s^{\frac{1}{7}}
s
7
5
⋅
s
7
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
1
7
⋅
b
1
7
b^{\frac{1}{7}} \cdot b^{\frac{1}{7}}
b
7
1
⋅
b
7
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
x
7
3
×
x
1
3
x^{\frac{7}{3}} \times x^{\frac{1}{3}}
x
3
7
×
x
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
______
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Simplify. Assume all variables are positive.
\newline
y
1
7
⋅
y
4
7
y^{\frac{1}{7}} \cdot y^{\frac{4}{7}}
y
7
1
⋅
y
7
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
______
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Simplify. Assume all variables are positive.
\newline
u
5
2
⋅
u
5
2
u^{\frac{5}{2}} \cdot u^{\frac{5}{2}}
u
2
5
⋅
u
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
______
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Simplify. Assume all variables are positive.
\newline
t
7
6
⋅
t
13
6
t^{\frac{7}{6}} \cdot t^{\frac{13}{6}}
t
6
7
⋅
t
6
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
______
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Simplify. Assume all variables are positive.
\newline
b
1
6
⋅
b
5
6
b^{\frac{1}{6}} \cdot b^{\frac{5}{6}}
b
6
1
⋅
b
6
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
d
9
7
⋅
d
8
7
d^{\frac{9}{7}} \cdot d^{\frac{8}{7}}
d
7
9
⋅
d
7
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
b
11
4
⋅
b
5
4
b^{\frac{11}{4}} \cdot b^{\frac{5}{4}}
b
4
11
⋅
b
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
______
Get tutor help
Simplify. Assume all variables are positive.
\newline
d
5
2
⋅
d
3
2
d^{\frac{5}{2}} \cdot d^{\frac{3}{2}}
d
2
5
⋅
d
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
5
2
⋅
r
5
2
r^{\frac{5}{2}} \cdot r^{\frac{5}{2}}
r
2
5
⋅
r
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
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