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Math Problems
Algebra 1
Multiplication with rational exponents
Which expression is equivalent to
(
x
+
2
x
2
)
(
x
+
2
3
x
)
?
\left(\frac{x+2}{x^{2}}\right)\left(\frac{x+2}{3 x}\right) ?
(
x
2
x
+
2
)
(
3
x
x
+
2
)
?
\newline
A.
x
2
+
4
3
x
2
\frac{x^{2}+4}{3 x^{2}}
3
x
2
x
2
+
4
\newline
B.
x
2
+
4
3
x
3
\frac{x^{2}+4}{3 x^{3}}
3
x
3
x
2
+
4
\newline
C.
x
2
+
4
x
+
4
3
x
2
\frac{x^{2}+4 x+4}{3 x^{2}}
3
x
2
x
2
+
4
x
+
4
\newline
D.
x
2
+
4
x
+
4
3
x
3
\frac{x^{2}+4 x+4}{3 x^{3}}
3
x
3
x
2
+
4
x
+
4
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0.375
0.25
\frac{0.375}{0.25}
0.25
0.375
का \(\left(\frac{\(3\)}{\(3\)}-\frac{\(2\)}{\(2\)}\right)+\frac{\(1\)}{\(4\)}+\frac{\(3\)}{\(4\)}\right)/\left(\frac{\(4\)}{\(4\)}+\frac{\(1\)}{\(2\)}\times\frac{\(4\)}{\(9\)}-\frac{\(1\)}{\(3\)}\right)
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
9
⋅
−
5
6
\frac{1}{9} \cdot-\frac{5}{6}
9
1
⋅
−
6
5
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1
9
⋅
−
5
6
\frac{1}{9} \cdot-\frac{5}{6}
9
1
⋅
−
6
5
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−
5
7
⋅
2
5
-\frac{5}{7} \cdot \frac{2}{5}
−
7
5
⋅
5
2
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(
−
(
9
2
)
)
/
(
(
9
7
)
)
\left(-\left(\frac{9}{2}\right)\right)/\left(\left(\frac{9}{7}\right)\right)
(
−
(
2
9
)
)
/
(
(
7
9
)
)
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Use the properties of exponents to simplify the expression. Write with positive exponents
\newline
d
3
7
⋅
d
3
7
d^{\frac{3}{7}} \cdot d^{\frac{3}{7}}
d
7
3
⋅
d
7
3
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If
x
=
4
(
5
+
1
)
(
5
4
+
1
)
(
5
8
+
1
)
(
5
16
+
1
)
x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}
x
=
(
5
+
1
)
(
4
5
+
1
)
(
8
5
+
1
)
(
16
5
+
1
)
4
then value of
(
1
+
x
)
48
(1+\mathrm{x})^{48}
(
1
+
x
)
48
is :-
\newline
(A)
25
25
25
\newline
(B)
50
50
50
\newline
(C)
125
125
125
\newline
(D)
500
500
500
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Which expression is equivalent to
3
(
8
b
)
3(8b)
3
(
8
b
)
?
\newline
Choices:
\newline
(A)
8
b
+
3
8b + 3
8
b
+
3
\newline
(B)
b
+
24
b + 24
b
+
24
\newline
(C)
b
+
11
b + 11
b
+
11
\newline
(D)
24
b
24b
24
b
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a)
2
x
−
5
4
−
x
−
4
3
=
x
4
\frac{2 x-5}{4}-\frac{x-4}{3}=\frac{x}{4}
4
2
x
−
5
−
3
x
−
4
=
4
x
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c.
2
−
3
⋅
□
3
=
10
□
2^{-3} \cdot \square^{3}=10 \square
2
−
3
⋅
□
3
=
10
□
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log
11
(
x
x
)
+
log
11
(
x
5
)
−
7
3
log
11
x
\log _{11}\left(\frac{x}{\sqrt{x}}\right)+\log _{11}\left(\sqrt{x^{5}}\right)-\frac{7}{3} \log _{11} x
lo
g
11
(
x
x
)
+
lo
g
11
(
x
5
)
−
3
7
lo
g
11
x
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{
1
4
x
−
1
3
y
=
3
2
1
4
x
+
3
4
y
=
5
2
\left\{\begin{array}{l}\frac{1}{4} x-\frac{1}{3} y=\frac{3}{2} \\ \frac{1}{4} x+\frac{3}{4} y=\frac{5}{2}\end{array}\right.
{
4
1
x
−
3
1
y
=
2
3
4
1
x
+
4
3
y
=
2
5
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15
a
28
5
−
7
a
20
7
2
a
4
35
\frac{15 \sqrt[5]{\sqrt[28]{a}}-7 \sqrt[7]{\sqrt[20]{a}}}{2 \sqrt[35]{\sqrt[4]{a}}}
2
35
4
a
15
5
28
a
−
7
7
20
a
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(
−
7
)
/
(
5
)
(-7)/(5)
(
−
7
)
/
(
5
)
^{
11
11
11
}\div((
−
7
-7
−
7
)/(
5
5
5
)\)^{
3
3
3
}=((
−
7
-7
−
7
)/(
5
5
5
)\)^{
2
2
2
n+
2
2
2
}
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Divide (using Complex Fractions -
\newline
(
5
6
x
+
3
)
(
1
6
−
y
)
\frac{\left(\frac{5}{6}x+3\right)}{\left(\frac{1}{6}-y\right)}
(
6
1
−
y
)
(
6
5
x
+
3
)
/
3
x
4
y
\frac{3x}{4y}
4
y
3
x
\newline
Paragraph
\newline
I
\newline
U_
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Divide (using Complex Fractions -
\newline
(
5
6
x
+
3
1
6
−
y
)
3
x
4
y
\frac{\left(\frac{\frac{5}{6} x+3}{\frac{1}{6}-y}\right)}{\frac{3 x}{4 y}}
4
y
3
x
(
6
1
−
y
6
5
x
+
3
)
\newline
Paragraph
\newline
B
\newline
I
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d
d
x
[
sin
(
e
x
+
a
2
)
]
\frac{\mathrm{d}}{\mathrm{d} x}\left[\sin \left(\frac{\sqrt{\mathrm{e}^{x}+a}}{2}\right)\right]
d
x
d
[
sin
(
2
e
x
+
a
)
]
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1
1
1
.
10
10
10
. Вычислите:
\newline
a)
1
2
−
1
5
\frac{1}{2}-\frac{1}{5}
2
1
−
5
1
\newline
б)
1
5
−
1
8
\frac{1}{5}-\frac{1}{8}
5
1
−
8
1
\newline
B)
1
8
−
1
11
\frac{1}{8}-\frac{1}{11}
8
1
−
11
1
\newline
г)
1
11
−
1
14
\frac{1}{11}-\frac{1}{14}
11
1
−
14
1
\newline
д)
1
14
−
1
17
;
\frac{1}{14}-\frac{1}{17} ;
14
1
−
17
1
;
\newline
e)
1
2
⋅
5
+
1
5
⋅
8
+
1
8
⋅
11
+
1
11
⋅
14
+
1
14
⋅
17
\frac{1}{2 \cdot 5}+\frac{1}{5 \cdot 8}+\frac{1}{8 \cdot 11}+\frac{1}{11 \cdot 14}+\frac{1}{14 \cdot 17}
2
⋅
5
1
+
5
⋅
8
1
+
8
⋅
11
1
+
11
⋅
14
1
+
14
⋅
17
1
\newline
ж)
1
1
⋅
4
+
1
4
⋅
7
+
1
7
⋅
10
+
1
10
⋅
13
+
1
13
⋅
16
\frac{1}{1 \cdot 4}+\frac{1}{4 \cdot 7}+\frac{1}{7 \cdot 10}+\frac{1}{10 \cdot 13}+\frac{1}{13 \cdot 16}
1
⋅
4
1
+
4
⋅
7
1
+
7
⋅
10
1
+
10
⋅
13
1
+
13
⋅
16
1
\newline
3
3
3
)
1
3
⋅
7
+
1
7
⋅
11
+
1
11
⋅
15
+
1
15
⋅
19
+
1
19
⋅
23
\frac{1}{3 \cdot 7}+\frac{1}{7 \cdot 11}+\frac{1}{11 \cdot 15}+\frac{1}{15 \cdot 19}+\frac{1}{19 \cdot 23}
3
⋅
7
1
+
7
⋅
11
1
+
11
⋅
15
1
+
15
⋅
19
1
+
19
⋅
23
1
.
\newline
2
2
2
.
78
78
78
. Упростите выражение:
\newline
a)
1
x
(
x
+
1
)
+
1
(
x
+
1
)
(
x
+
2
)
+
1
(
x
+
2
)
(
x
+
3
)
+
1
(
x
+
3
)
(
x
+
4
)
+
1
(
x
+
4
)
(
x
+
5
)
\frac{1}{x(x+1)}+\frac{1}{(x+1)(x+2)}+\frac{1}{(x+2)(x+3)}+\frac{1}{(x+3)(x+4)}+\frac{1}{(x+4)(x+5)}
x
(
x
+
1
)
1
+
(
x
+
1
)
(
x
+
2
)
1
+
(
x
+
2
)
(
x
+
3
)
1
+
(
x
+
3
)
(
x
+
4
)
1
+
(
x
+
4
)
(
x
+
5
)
1
;
\newline
6
6
6
)
1
x
(
x
+
3
)
+
1
(
x
+
3
)
(
x
+
6
)
+
1
(
x
+
6
)
(
x
+
9
)
+
1
(
x
+
9
)
(
x
+
12
)
+
1
(
x
+
12
)
(
x
+
15
)
\frac{1}{x(x+3)}+\frac{1}{(x+3)(x+6)}+\frac{1}{(x+6)(x+9)}+\frac{1}{(x+9)(x+12)}+\frac{1}{(x+12)(x+15)}
x
(
x
+
3
)
1
+
(
x
+
3
)
(
x
+
6
)
1
+
(
x
+
6
)
(
x
+
9
)
1
+
(
x
+
9
)
(
x
+
12
)
1
+
(
x
+
12
)
(
x
+
15
)
1
.
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Q
9
9
9
. Anya uses
3
2
kg
\frac{3}{2}\,\text{kg}
2
3
kg
of flour,
8
3
kg
\frac{8}{3}\,\text{kg}
3
8
kg
of cheese and
1
4
kg
\frac{1}{4}\,\text{kg}
4
1
kg
of pepperoni to make pizza. Find the total mass of ingredients she uses?
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3
4
x
−
3
4
≥
−
6
\frac{3}{4}x-\frac{3}{4} \geq -6
4
3
x
−
4
3
≥
−
6
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Dante took
5
1
2
5 \frac{1}{2}
5
2
1
hours to clean the bathroom. He took
3
2
5
3 \frac{2}{5}
3
5
2
hours to clean the bedroom. How much longer did it take Dante to clean the bathroom?
\newline
Write your answer as a mixed number in simplest form.
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A farmer's land is separated into sections of size
2
3
7
2 \frac{3}{7}
2
7
3
acres. Suppose there are
2
4
5
2 \frac{4}{5}
2
5
4
such sections. How many acres of land does the farmer own?
\newline
Write your answer as a mixed number in simplest form.
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5
w
7
w
4
\frac{5w}{7w^{4}}
7
w
4
5
w
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Select the expressions that are equivalent to
6
(
r
+
8
)
6(r + 8)
6
(
r
+
8
)
.
\newline
Multi-select Choices:
\newline
(A)
48
r
+
6
48r + 6
48
r
+
6
\newline
(B)
8
(
6
+
r
)
8(6 + r)
8
(
6
+
r
)
\newline
(C)
(
r
×
8
)
6
(r \times 8)6
(
r
×
8
)
6
\newline
(D)
6
r
+
48
6r + 48
6
r
+
48
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(
2
3
)
−
4
÷
(
6
4
)
−
2
\left(\frac{2}{3}\right)^{-4} \div\left(\frac{6}{4}\right)^{-2}
(
3
2
)
−
4
÷
(
4
6
)
−
2
Get tutor help
5
2
∗
5
6
5^{2} * 5^{6}
5
2
∗
5
6
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Simplify:
1
9
x
9
8
x
3
\frac{\frac{1}{9x}}{\frac{9}{8x^{3}}}
8
x
3
9
9
x
1
Get tutor help
(
10
)
(
1
)
∗
∗
(
10
)
(
3
)
∗
∗
(
10
)
(
5
)
(10)^{(1)}**(10)^{(3)}**(10)^{(5)}
(
10
)
(
1
)
∗
∗
(
10
)
(
3
)
∗
∗
(
10
)
(
5
)
Get tutor help
(
y
−
2
)
−
6
−
x
4
y
−
4
⋅
−
x
y
4
\frac{\left(y^{-2}\right)^{-6}}{-x^{4} y^{-4} \cdot-x y^{4}}
−
x
4
y
−
4
⋅−
x
y
4
(
y
−
2
)
−
6
Get tutor help
4
x
y
−
2
−
3
y
x
2
⋅
−
2
y
0
\frac{4 x y^{-2}}{-3 y x^{2} \cdot-2 y^{0}}
−
3
y
x
2
⋅−
2
y
0
4
x
y
−
2
Get tutor help
(
b
2
−
2
b
5
⋅
a
b
2
)
0
\left(\frac{b^{2}}{-2 b^{5} \cdot a b^{2}}\right)^{0}
(
−
2
b
5
⋅
a
b
2
b
2
)
0
Get tutor help
−
4
x
3
⋅
x
2
y
4
−
2
x
3
y
4
\frac{-4 x^{3} \cdot x^{2} y^{4}}{-2 x^{3} y^{4}}
−
2
x
3
y
4
−
4
x
3
⋅
x
2
y
4
Get tutor help
Which expressions are equivalent to
\newline
5
2
5
8
\frac{5^{2}}{5^{8}}
5
8
5
2
?
\newline
Choose
2
2
2
answers:
\newline
A
1
5
6
\frac{1}{5^{6}}
5
6
1
\newline
B
1
−
6
1^{-6}
1
−
6
\newline
C.
(
5
2
)
−
3
(5^{2})^{-3}
(
5
2
)
−
3
\newline
D
(
5
2
)
−
8
(5^{2})^{-8}
(
5
2
)
−
8
Get tutor help
What is the slope of the line?
\newline
2
x
−
5
y
=
9
2x-5y=9
2
x
−
5
y
=
9
\newline
Choose
1
1
1
answer:
\newline
(A)
5
2
\frac{5}{2}
2
5
\newline
(B)
2
5
\frac{2}{5}
5
2
\newline
(C)
−
5
2
-\frac{5}{2}
−
2
5
\newline
(D)
−
2
5
-\frac{2}{5}
−
5
2
Get tutor help
Select the equivalent expression.
\newline
(
3
−
8
⋅
7
3
)
−
2
=
(3^{-8}\cdot7^{3})^{-2}=
(
3
−
8
⋅
7
3
)
−
2
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
7
6
3
16
\frac{7^{6}}{3^{16}}
3
16
7
6
\newline
(B)
\newline
2
1
10
21^{10}
2
1
10
\newline
(C)
\newline
3
16
⋅
7
−
6
3^{16}\cdot7^{-6}
3
16
⋅
7
−
6
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(
2
y
4
)
3
(
5
y
6
)
2
=
\left(2 y^{4}\right)^{3}\left(5 y^{6}\right)^{2}=
(
2
y
4
)
3
(
5
y
6
)
2
=
Get tutor help
Determine the convergence or divergence of the series.
\newline
1
+
1
4
3
+
1
9
3
+
1
16
3
+
1
25
3
+
…
1+\frac{1}{\sqrt[3]{4}}+\frac{1}{\sqrt[3]{9}}+\frac{1}{\sqrt[3]{16}}+\frac{1}{\sqrt[3]{25}}+\dots
1
+
3
4
1
+
3
9
1
+
3
16
1
+
3
25
1
+
…
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6
6
6
. Which expression is equivalent to
\newline
3
2
8
y
16
4
⋅
2
2
6
y
12
6
⋅
2
24
y
16
8
where
y
>
0
?
3 \sqrt[4]{2^{8} y^{16}} \cdot 2 \sqrt[6]{2^{6} y^{12}} \cdot \sqrt[8]{2^{24} y^{16}} \text { where } y>0 ?
3
4
2
8
y
16
⋅
2
6
2
6
y
12
⋅
8
2
24
y
16
where
y
>
0
?
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(
1
3
)
−
2
÷
(
3
5
)
−
3
\left(\frac{1}{3}\right)^{-2} \div\left(\frac{3}{5}\right)^{-3}
(
3
1
)
−
2
÷
(
5
3
)
−
3
Get tutor help
x
=
1
2
2
+
2
2
+
2
+
2
2
+
2
+
2
2
x=\frac{\frac{\frac{1}{2}}{2+2}}{\frac{2+2+2}{\frac{2+2+2}{2}}}
x
=
2
2
+
2
+
2
2
+
2
+
2
2
+
2
2
1
Get tutor help
1
2
2
+
2
2
+
2
+
2
2
+
2
+
2
2
+
2
\frac{\frac{\frac{1}{2}}{2+2}}{\frac{2+2+2}{\frac{2+2+2}{2+2}}}
2
+
2
2
+
2
+
2
2
+
2
+
2
2
+
2
2
1
Get tutor help
A bowl contains
12
12
12
green candies,
4
4
4
yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random?
\newline
E.
\newline
(
2
)
/
(
11
)
(2)/(11)
(
2
)
/
(
11
)
\newline
F.
\newline
(
2
)
/
(
9
)
(2)/(9)
(
2
)
/
(
9
)
\newline
G.
\newline
(
1
)
/
(
4
)
(1)/(4)
(
1
)
/
(
4
)
\newline
H.
\newline
(
3
)
/
(
11
)
(3)/(11)
(
3
)
/
(
11
)
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Complete the equation. Write the sum as a mixed number.
\newline
4
3
+
2
7
=
28
21
+
14
21
=
□
42
21
\frac{4}{3}+\frac{2}{7}=\frac{28}{21}+\frac{14}{21}=\square \frac{42}{21}
3
4
+
7
2
=
21
28
+
21
14
=
□
21
42
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Complete the equation. Write the sum as a mixed number.
\newline
2
2
3
+
4
5
=
40
□
+
12
□
=
□
□
□
2 \frac{2}{3}+\frac{4}{5}=\frac{40}{\square}+\frac{12}{\square}=\square \frac{\square}{\square}
2
3
2
+
5
4
=
□
40
+
□
12
=
□
□
□
Get tutor help
Complete the equation. Write the sum as a mixed number.
\newline
4
3
+
2
7
=
□
21
+
□
21
=
□
□
□
\frac{4}{3}+\frac{2}{7}=\frac{\square}{21}+\frac{\square}{21}=\square \frac{\square}{\square}
3
4
+
7
2
=
21
□
+
21
□
=
□
□
□
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2
1
2
×
2
3
4
×
3
×
3
3
2
2
1
2
×
3
−
1
2
\frac{2^{\frac{1}{2}}\times2^{\frac{3}{4}}\times3\times3^{\frac{3}{2}}}{2^{\frac{1}{2}}\times3^{-\frac{1}{2}}}
2
2
1
×
3
−
2
1
2
2
1
×
2
4
3
×
3
×
3
2
3
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2
−
1
+
5
×
4
−
(
5
−
1
)
2-1+5\times 4-(5-1)
2
−
1
+
5
×
4
−
(
5
−
1
)
Get tutor help
x
8
3
x
⋅
x
1
2
\frac{x^{\frac{8}{3}}}{x \cdot x^{\frac{1}{2}}}
x
⋅
x
2
1
x
3
8
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Question
\newline
Perform the operation and combine to one fraction.
\newline
3
x
+
5
x
+
7
+
3
x
+
5
\frac{3 x+5}{x+7}+\frac{3}{x+5}
x
+
7
3
x
+
5
+
x
+
5
3
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1
2
3
...
21
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