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Math Problems
Algebra 1
Multiplication with rational exponents
Find
−
5
7
−
2
2
3
-\frac{5}{7}-2 \frac{2}{3}
−
7
5
−
2
3
2
. Write your answer as a fraction.
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2
3
−
2
x
x
−
3
x
\frac{\frac{2}{3}-\frac{2}{x}}{\frac{x-3}{x}}
x
x
−
3
3
2
−
x
2
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Rewrite the expression in the form
k
⋅
z
n
k \cdot z^{n}
k
⋅
z
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
3
z
4
⋅
3
z
3
4
=
3 \sqrt[4]{z} \cdot 3 z^{\frac{3}{4}}=
3
4
z
⋅
3
z
4
3
=
\newline
□
\square
□
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Which expressions are equivalent to
4
−
3
4
−
1
\frac{4^{-3}}{4^{-1}}
4
−
1
4
−
3
?
\newline
Choose
2
2
2
answers:
\newline
(A)
4
1
4
3
\frac{4^{1}}{4^{3}}
4
3
4
1
\newline
B
1
4
2
\frac{1}{4^{2}}
4
2
1
\newline
(c)
4
3
⋅
4
1
4^{3} \cdot 4^{1}
4
3
⋅
4
1
\newline
D
(
4
−
1
)
−
3
\left(4^{-1}\right)^{-3}
(
4
−
1
)
−
3
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Which of the following expressions are equivalent to
\newline
J
−
k
\frac{J}{-k}
−
k
J
?
\newline
Choose all answers that apply:
\newline
A
\newline
−
j
−
k
-\frac{j}{-k}
−
−
k
j
\newline
(B)
\newline
−
−
j
k
-\frac{-j}{k}
−
k
−
j
\newline
(c) None of the above
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Simplify. Express your answer using positive exponents.
\newline
6
t
−
1
t
−
1
⋅
t
−
1
\frac{6 t^{-1}}{t^{-1} \cdot t^{-1}}
t
−
1
⋅
t
−
1
6
t
−
1
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Which of the following is equivalent to
(
3
+
3
a
)
(
3
a
)
\frac{\left(3+\frac{3}{a}\right)}{\left(\frac{3}{a}\right)}
(
a
3
)
(
3
+
a
3
)
?
\newline
(A)
a
+
1
a+1
a
+
1
\newline
(B)
a
a
a
\newline
(C)
2
2
2
\newline
(D)
1
2
\frac{1}{2}
2
1
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(
4
3
5
−
2
)
5
⇒
?
\left(\frac{4^{3}}{5^{-2}}\right)^{5} \Rightarrow ?
(
5
−
2
4
3
)
5
⇒
?
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Which of the following expressions are equivalent to
6.53
−
(
−
4.11
)
+
7.92
6.53 - (-4.11) + 7.92
6.53
−
(
−
4.11
)
+
7.92
?
\newline
A)
6.53
+
4.11
+
7.92
6.53 + 4.11 + 7.92
6.53
+
4.11
+
7.92
\newline
B)
−
(
−
6.53
)
+
4.11
−
(
−
7.92
)
-(-6.53)+4.11-(-7.92)
−
(
−
6.53
)
+
4.11
−
(
−
7.92
)
\newline
C)
−
4.11
−
6.53
+
7.92
-4.11-6.53+7.92
−
4.11
−
6.53
+
7.92
\newline
D)
4.11
−
6.53
+
7.92
4.11-6.53+7.92
4.11
−
6.53
+
7.92
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Select the equivalent expression.
\newline
1
k
8
⋅
k
3
33
\sqrt[33]{\frac{1}{k^{8} \cdot k^{3}}}
33
k
8
⋅
k
3
1
\newline
(A)
k
−
3
k^{-3}
k
−
3
\newline
(B)
k
3
k^{3}
k
3
r
\newline
(C)
k
1
3
k^{\frac{1}{3}}
k
3
1
\newline
(D)
k
−
1
3
k^{-\frac{1}{3}}
k
−
3
1
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Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).
\newline
lim
x
→
∞
−
27
x
7
−
x
12
3
8
x
2
+
x
+
8
x
4
\lim _{x \rightarrow \infty} \frac{\sqrt[3]{-27 x^{7}-x^{12}}}{8 x^{2}+x+8 x^{4}}
x
→
∞
lim
8
x
2
+
x
+
8
x
4
3
−
27
x
7
−
x
12
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If
3
x
+
4
y
=
7
3x+4y=7
3
x
+
4
y
=
7
, which of the following expressions is equivalent to
y
y
y
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
x
+
7
-3x+7
−
3
x
+
7
\newline
(B)
−
3
4
x
\frac{-3}{4}x
4
−
3
x
+
+
+
7
4
\frac{7}{4}
4
7
\newline
(C)
3
4
x
\frac{3}{4}x
4
3
x
+
+
+
7
4
\frac{7}{4}
4
7
\newline
(D)
3
x
+
7
3x+7
3
x
+
7
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What is the slope of the line?
\newline
y
+
1
=
3
(
x
−
4
)
y+1=3(x-4)
y
+
1
=
3
(
x
−
4
)
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
\frac{1}{3}
3
1
\newline
(B)
−
4
3
-\frac{4}{3}
−
3
4
\newline
(C)
−
3
4
-\frac{3}{4}
−
4
3
\newline
(D)
3
3
3
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Find the value of
A
A
A
that makes the following equation true for all values of
x
x
x
.
\newline
2
x
=
A
(
x
12
)
2^{x}=A^{\left(\frac{x}{12}\right)}
2
x
=
A
(
12
x
)
\newline
Choose
1
1
1
answer:
\newline
(A)
A
=
2
×
12
A=2\times 12
A
=
2
×
12
\newline
(B)
A
=
2
(
1
12
)
A=2^{\left(\frac{1}{12}\right)}
A
=
2
(
12
1
)
\newline
(C)
A
=
2
12
A=2^{12}
A
=
2
12
\newline
(D)
A
=
(
1
12
)
2
A=\left(\frac{1}{12}\right)^{2}
A
=
(
12
1
)
2
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Which of these are equal to
10
10
10
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
110
−
11
\frac{110}{-11}
−
11
110
\newline
(B)
−
110
−
11
-\frac{110}{-11}
−
−
11
110
\newline
(C)
−
110
11
-\frac{110}{11}
−
11
110
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Subtract:
11
12
−
13
16
\frac{11}{12}-\frac{13}{16}
12
11
−
16
13
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Use the model to find the product.
\newline
1
4
×
1
4
=
‾
/
‾
\frac{1}{4} \times \frac{1}{4} = \underline{\hspace{1cm}}/\underline{\hspace{1cm}}
4
1
×
4
1
=
/
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(
−
12
)
×
(
−
11
)
×
(
10
)
(-12)\times(-11)\times(10)
(
−
12
)
×
(
−
11
)
×
(
10
)
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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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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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−
5
7
⋅
2
5
-\frac{5}{7} \cdot \frac{2}{5}
−
7
5
⋅
5
2
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Solve:
(
−
(
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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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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Solve for
n
n
n
:
(
−
7
5
)
11
(\frac{-7}{5})^{11}
(
5
−
7
)
11
÷
÷
÷
(
−
7
5
)
3
(\frac{-7}{5})^{3}
(
5
−
7
)
3
=
=
=
(
−
7
5
)
2
n
+
2
(\frac{-7}{5})^{2n+2}
(
5
−
7
)
2
n
+
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
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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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Solve for
x
x
x
:
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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Simplify the expression:
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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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
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Multiply the expression:
(
10
)
(
1
)
∗
(
10
)
(
3
)
∗
(
10
)
(
5
)
(10)^{(1)}*(10)^{(3)}*(10)^{(5)}
(
10
)
(
1
)
∗
(
10
)
(
3
)
∗
(
10
)
(
5
)
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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
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(
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
=
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−
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
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
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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
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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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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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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.
(
2
)
/
(
11
)
(2)/(11)
(
2
)
/
(
11
)
\newline
F.
(
2
)
/
(
9
)
(2)/(9)
(
2
)
/
(
9
)
\newline
G.
(
1
)
/
(
4
)
(1)/(4)
(
1
)
/
(
4
)
\newline
H.
(
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
Get tutor help
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
□
=
□
□
□
Get tutor help
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2
3
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