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Let’s check out your problem:
Perform the operation and simplify the answer fully.
\newline
10
7
⋅
1
2
\frac{10}{7} \cdot \frac{1}{2}
7
10
⋅
2
1
\newline
Answer:
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Home
Math Problems
Precalculus
Operations with rational exponents
Full solution
Q.
Perform the operation and simplify the answer fully.
\newline
10
7
⋅
1
2
\frac{10}{7} \cdot \frac{1}{2}
7
10
⋅
2
1
\newline
Answer:
Identify Operation:
Identify the operation to be performed.
\newline
We need to multiply the two
fractions
(
10
7
)
(\frac{10}{7})
(
7
10
)
and
(
1
2
)
(\frac{1}{2})
(
2
1
)
.
Multiply Numerators and Denominators:
Multiply the numerators and then the denominators.
\newline
(
10
7
)
×
(
1
2
)
=
(
10
×
1
7
×
2
)
(\frac{10}{7}) \times (\frac{1}{2}) = (\frac{10 \times 1}{7 \times 2})
(
7
10
)
×
(
2
1
)
=
(
7
×
2
10
×
1
)
Perform Multiplication:
Perform the multiplication.
\newline
10
×
1
=
10
10 \times 1 = 10
10
×
1
=
10
\newline
7
×
2
=
14
7 \times 2 = 14
7
×
2
=
14
\newline
So,
(
10
/
7
)
×
(
1
/
2
)
=
10
/
14
(10/7) \times (1/2) = 10/14
(
10/7
)
×
(
1/2
)
=
10/14
Simplify Fraction:
Simplify the
fraction
by finding the greatest common divisor (GCD) of the numerator and the denominator.
\newline
The GCD of
10
10
10
and
14
14
14
is
2
2
2
.
Divide by GCD:
Divide both the numerator and the denominator by the GCD to simplify the fraction.
\newline
10
÷
2
=
5
10 \div 2 = 5
10
÷
2
=
5
\newline
14
÷
2
=
7
14 \div 2 = 7
14
÷
2
=
7
\newline
So,
10
14
\frac{10}{14}
14
10
simplifies to
5
7
\frac{5}{7}
7
5
.
More problems from Operations with rational exponents
Question
f
(
x
)
=
6
x
+
5
2
−
14
+
5
x
f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}}
f
(
x
)
=
2
−
14
+
5
x
6
x
+
5
\newline
We want to find
lim
x
→
−
2
f
(
x
)
\lim _{x \rightarrow-2} f(x)
lim
x
→
−
2
f
(
x
)
.
\newline
What happens when we use direct substitution?
\newline
Choose
1
1
1
answer:
\newline
(A) The limit exists, and we found it!
\newline
(B) The limit doesn't exist (probably an asymptote).
\newline
(C) The result is indeterminate.
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\newline
What is the value of
d
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d
x
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\frac{d^{2} y}{d x^{2}}
d
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d
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)
(-2,1)
(
−
2
,
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)
?
\newline
Give an exact number.
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Question
What is the area of the region bound by the graphs of
f
(
x
)
=
x
−
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,
g
(
x
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−
x
f(x)=\sqrt{x-2}, g(x)=14-x
f
(
x
)
=
x
−
2
,
g
(
x
)
=
14
−
x
, and
x
=
2
x=2
x
=
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
19
6
\frac{19}{6}
6
19
\newline
(B)
99
2
\frac{99}{2}
2
99
\newline
(C)
151
2
\frac{151}{2}
2
151
\newline
(D)
45
2
\frac{45}{2}
2
45
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Question
Let
g
(
x
)
=
x
4
3
g(x)=x^{\frac{4}{3}}
g
(
x
)
=
x
3
4
.
\newline
g
′
(
27
)
=
g^{\prime}(27)=
g
′
(
27
)
=
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Question
Simplify
ln
(
1
e
)
\ln \left(\frac{1}{\sqrt{e}}\right)
ln
(
e
1
)
\newline
Answer:
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Question
Simplify
ln
(
1
e
)
\ln \left(\frac{1}{e}\right)
ln
(
e
1
)
\newline
Answer:
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y
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y
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(
sin
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5
x
2
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\left(10x^{3}-5x^{2}-6x\right)\div\left(2x^{2}\right)
(
10
x
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x
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x
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2
x
2
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Question
y
=
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4
x
sin
4
x
y=\cos^{4}x\sin^{4}x
y
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4
x
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Question
3
5
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3
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3
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