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Math Problems
Algebra 1
Simplify exponential expressions using the multiplication and division rules
Which numbers are not in the solution set of the inequality
−
0.5
m
−
0.2
<
0.3
(
2
−
m
)
-0.5m - 0.2 < 0.3(2 - m)
−
0.5
m
−
0.2
<
0.3
(
2
−
m
)
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
−
4
-4
−
4
\newline
(B)
0
0
0
\newline
(C)
3
3
3
\newline
(D)
−
6
-6
−
6
\newline
(E)
−
9
2
-\frac{9}{2}
−
2
9
\newline
(F)
−
2
-2
−
2
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Which numbers are in the solution set of the inequality
3
4
(
2
+
2
3
k
)
>
−
1
2
(
3
k
−
2
)
\frac{3}{4}(2 + \frac{2}{3}k) > -\frac{1}{2}(3k - 2)
4
3
(
2
+
3
2
k
)
>
−
2
1
(
3
k
−
2
)
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
−
1
4
-\frac{1}{4}
−
4
1
\newline
(B)
0
0
0
\newline
(C)
1
2
\frac{1}{2}
2
1
\newline
(D)
−
1
2
-\frac{1}{2}
−
2
1
\newline
(E)
−
6
-6
−
6
\newline
(F)
−
3
-3
−
3
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Factor the trinomial.
\newline
8
x
2
−
5
x
+
5
y
+
24
y
2
8x^{2}-5x+5y+24y^{2}
8
x
2
−
5
x
+
5
y
+
24
y
2
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Simplify. Express your answer using positive exponents.
\newline
(
7
u
)
(
2
u
)
(
5
u
4
)
(7u)(2u)(5u^4)
(
7
u
)
(
2
u
)
(
5
u
4
)
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Simplify. Express your answer using positive exponents.
\newline
8
j
5
(
8
j
6
)
(
j
)
\frac{8j^5}{(8j^6)(j)}
(
8
j
6
)
(
j
)
8
j
5
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Simplify. Express your answer using positive exponents.
\newline
10
b
7
5
b
⋅
b
6
\frac{10b^7}{5b \cdot b^6}
5
b
⋅
b
6
10
b
7
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Simplify. Express your answer using positive exponents.
\newline
(
6
j
)
(
8
j
)
(
6
j
9
)
(6j)(8j)(6j^9)
(
6
j
)
(
8
j
)
(
6
j
9
)
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Simplify. Express your answer using positive exponents.
\newline
(
4
z
4
)
(
4
z
4
)
(
10
z
2
)
(4z^4)(4z^4)(10z^2)
(
4
z
4
)
(
4
z
4
)
(
10
z
2
)
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Simplify. Express your answer using positive exponents.
\newline
8
j
8
4
j
3
⋅
j
3
\frac{8j^8}{4j^3 \cdot j^3}
4
j
3
⋅
j
3
8
j
8
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Simplify. Express your answer using positive exponents.
\newline
2
y
7
2
y
⋅
y
8
\frac{2y^7}{2y \cdot y^8}
2
y
⋅
y
8
2
y
7
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Simplify. Express your answer using positive exponents.
\newline
2
z
2
(
2
z
9
)
(
z
6
)
\frac{2z^2}{(2z^9)(z^6)}
(
2
z
9
)
(
z
6
)
2
z
2
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Simplify. Express your answer using positive exponents.
\newline
(
4
s
2
)
(
4
s
7
)
(
3
s
6
)
(4s^2)(4s^7)(3s^6)
(
4
s
2
)
(
4
s
7
)
(
3
s
6
)
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Simplify. Express your answer using positive exponents.
\newline
3
p
(
3
p
9
)
(
p
8
)
\frac{3p}{(3p^9)(p^8)}
(
3
p
9
)
(
p
8
)
3
p
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Use exponent laws to simplify
(
x
8
)
(
x
3
5
)
(\sqrt[8]{x})\left(\sqrt[5]{x^{3}}\right)
(
8
x
)
(
5
x
3
)
.
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Simplify. Write your answer using whole numbers and variables.
\newline
5
n
2
−
3
n
5
n
−
3
\frac{5n^2 - 3n}{5n - 3}
5
n
−
3
5
n
2
−
3
n
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Simplify. Write your answer using whole numbers and variables.
\newline
13
p
+
26
p
+
2
\frac{13p + 26}{p + 2}
p
+
2
13
p
+
26
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Simplify by combining like terms.
\newline
21
b
−
32
+
7
b
−
20
b
−
20
21 b-32+7 b-20 b-20
21
b
−
32
+
7
b
−
20
b
−
20
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Simplify. Express your answer using positive exponents.
\newline
7
u
9
⋅
2
u
2
⋅
7
u
7 u^{9} \cdot 2 u^{2} \cdot 7 u
7
u
9
⋅
2
u
2
⋅
7
u
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Simplify. Express your answer using positive exponents.
\newline
7
p
7
p
\frac{7p}{7p}
7
p
7
p
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Simplify. Express your answer using positive exponents.
\newline
4
z
4
z
\frac{4z}{4z}
4
z
4
z
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Select all of the equations below that are equivalent to:
\newline
12
g
=
8
12g = 8
12
g
=
8
\newline
Use properties of equality.
\newline
\newline
Multi-select Choices:
\newline
(A)
12
g
−
3
=
4
12g - 3 = 4
12
g
−
3
=
4
\newline
(B)
12
g
−
2
=
7
12g - 2 = 7
12
g
−
2
=
7
\newline
(C)
12
g
−
3
=
5
12g - 3 = 5
12
g
−
3
=
5
\newline
(D)
12
g
−
4
=
2
12g - 4 = 2
12
g
−
4
=
2
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Select all of the equations below that are equivalent to:
\newline
p
q
=
11
pq = 11
pq
=
11
\newline
Use properties of equality.
\newline
Multi-select Choices:
\newline
(A)
9
+
p
q
=
20
9 + pq = 20
9
+
pq
=
20
\newline
(B)
4
+
p
q
=
15
4 + pq = 15
4
+
pq
=
15
\newline
(C)
p
q
+
7
=
18
pq + 7 = 18
pq
+
7
=
18
\newline
(D)
2
+
p
q
=
13
2 + pq = 13
2
+
pq
=
13
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Select all of the equations below that are equivalent to:
\newline
r
s
=
22
rs = 22
rs
=
22
\newline
Use properties of equality.
\newline
Multi-select Choices:
\newline
(A)
r
s
11
=
2
\frac{rs}{11} = 2
11
rs
=
2
\newline
(B)
r
s
11
=
4
\frac{rs}{11} = 4
11
rs
=
4
\newline
(C)
r
s
−
11
=
−
3
\frac{rs}{-11} = -3
−
11
rs
=
−
3
\newline
(D)
r
s
2
=
11
\frac{rs}{2} = 11
2
rs
=
11
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Select all of the equations below that are equivalent to:
\newline
3
+
h
=
7
3 + h = 7
3
+
h
=
7
\newline
Use properties of equality.
\newline
Multi-select Choices:
\newline
(A)
3
+
h
+
10
=
15
3 + h + 10 = 15
3
+
h
+
10
=
15
\newline
(B)
3
+
h
+
3
=
10
3 + h + 3 = 10
3
+
h
+
3
=
10
\newline
(C)
14
+
h
=
12
+
7
14 + h = 12 + 7
14
+
h
=
12
+
7
\newline
(D)
8
+
h
=
4
+
7
8 + h = 4 + 7
8
+
h
=
4
+
7
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Select all of the equations below that are equivalent to:
\newline
f
g
=
8
fg = 8
f
g
=
8
\newline
Use properties of equality.
\newline
Multi-select Choices:
\newline
(A)
10
+
f
g
=
18
10 + fg = 18
10
+
f
g
=
18
\newline
(B)
f
g
+
3
=
11
fg + 3 = 11
f
g
+
3
=
11
\newline
(C)
f
g
+
4
=
12
fg + 4 = 12
f
g
+
4
=
12
\newline
(D)
12
+
f
g
=
20
12 + fg = 20
12
+
f
g
=
20
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Simplify. Express your answer using positive exponents.
\newline
(
9
q
)
(
5
q
)
(
6
q
7
)
(9q)(5q)(6q^7)
(
9
q
)
(
5
q
)
(
6
q
7
)
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Simplify. Express your answer using positive exponents.
\newline
6
s
(
3
s
)
(
s
2
)
\frac{6s}{(3s)(s^2)}
(
3
s
)
(
s
2
)
6
s
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Simplify. Express your answer using positive exponents.
\newline
9
a
6
a
3
⋅
3
a
\frac{9a^6}{a^3 \cdot 3a}
a
3
⋅
3
a
9
a
6
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Simplify. Express your answer using positive exponents.
\newline
6
f
3
2
f
⋅
f
3
\frac{6f^3}{2f \cdot f^3}
2
f
⋅
f
3
6
f
3
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Simplify. Express your answer using positive exponents.
\newline
3
h
(
3
h
)
(
h
7
)
\frac{3h}{(3h)(h^7)}
(
3
h
)
(
h
7
)
3
h
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Simplify. Express your answer using positive exponents.
\newline
7
w
w
7
⋅
7
w
\frac{7w}{w^7 \cdot 7w}
w
7
⋅
7
w
7
w
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Simplify. Express your answer using positive exponents.
\newline
9
u
4
(
u
)
(
3
u
)
\frac{9u^4}{(u)(3u)}
(
u
)
(
3
u
)
9
u
4
Get tutor help
Simplify. Express your answer using positive exponents.
\newline
(
4
t
)
(
10
t
)
(
7
t
)
(4t)(10t)(7t)
(
4
t
)
(
10
t
)
(
7
t
)
Get tutor help
Simplify. Express your answer using positive exponents.
\newline
5
n
8
(
5
n
4
)
(
n
9
)
\frac{5n^8}{(5n^4)(n^9)}
(
5
n
4
)
(
n
9
)
5
n
8
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Simplify. Express your answer using positive exponents.
\newline
6
y
4
2
y
4
⋅
y
8
\frac{6y^4}{2y^4 \cdot y^8}
2
y
4
⋅
y
8
6
y
4
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Simplify. Express your answer using positive exponents.
\newline
4
k
2
(
2
k
5
)
(
k
)
\frac{4k^2}{(2k^5)(k)}
(
2
k
5
)
(
k
)
4
k
2
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Simplify. Express your answer using positive exponents.
\newline
5
n
7
5
n
⋅
n
\frac{5n^7}{5n \cdot n}
5
n
⋅
n
5
n
7
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Simplify. Express your answer using positive exponents.
\newline
9
s
2
3
s
⋅
s
\frac{9s^2}{3s \cdot s}
3
s
⋅
s
9
s
2
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Simplify. Express your answer using positive exponents.
\newline
6
y
(
2
y
)
(
y
5
)
\frac{6y}{(2y)(y^5)}
(
2
y
)
(
y
5
)
6
y
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Simplify. Express your answer using positive exponents.
\newline
(
8
j
)
(
9
j
)
(
4
j
)
(8j)(9j)(4j)
(
8
j
)
(
9
j
)
(
4
j
)
Get tutor help
Simplify. Express your answer using positive exponents.
\newline
(
6
w
)
(
2
w
)
(
8
w
4
)
(6w)(2w)(8w^4)
(
6
w
)
(
2
w
)
(
8
w
4
)
Get tutor help
Simplify. Express your answer using positive exponents.
\newline
4
u
6
u
⋅
4
u
\frac{4u^6}{u \cdot 4u}
u
⋅
4
u
4
u
6
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Simplify. Express your answer using positive exponents.
\newline
(
7
z
7
)
(
9
z
2
)
(
5
z
4
)
(7z^7)(9z^2)(5z^4)
(
7
z
7
)
(
9
z
2
)
(
5
z
4
)
Get tutor help
Simplify. Express your answer using positive exponents.
\newline
(
8
t
)
(
5
t
)
(
5
t
)
(8t)(5t)(5t)
(
8
t
)
(
5
t
)
(
5
t
)
Get tutor help
Simplify. Express your answer using positive exponents.
\newline
(
10
n
)
(
6
n
)
(
9
n
4
)
(10n)(6n)(9n^4)
(
10
n
)
(
6
n
)
(
9
n
4
)
Get tutor help
Which of the following is a natural number?
\newline
Choices:
\newline
(A)
−
13
4
-\frac{13}{4}
−
4
13
\newline
(B)
7
7
7
\newline
(C)
−
1
-1
−
1
\newline
(D)
6
7
\frac{6}{7}
7
6
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Which of the following are irrational numbers?
\newline
Multi-select Choices:
\newline
(A)
5
5
5
\newline
(B)
2
2
2
\newline
(C)
6
6
6
\newline
(D)
5
5
5
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Which of the following are irrational numbers?
\newline
Multi-select Choices:
\newline
(A)
7
7
7
\newline
(B)
2
2
2
\newline
(C)
7
\sqrt{7}
7
\newline
(D)
0
0
0
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What is the area of the region between the graphs of
f
(
x
)
=
4
x
f(x)=\frac{4}{x}
f
(
x
)
=
x
4
,
g
(
x
)
=
4
g(x)=4
g
(
x
)
=
4
, and
x
=
4
x=4
x
=
4
?
\newline
Choose
1
1
1
answer:
\newline
(A)
24
−
4
ln
(
4
)
24-4 \ln (4)
24
−
4
ln
(
4
)
\newline
(B)
12
−
4
ln
(
3
)
12-4 \ln (3)
12
−
4
ln
(
3
)
\newline
(C)
12
−
4
ln
(
4
)
12-4 \ln (4)
12
−
4
ln
(
4
)
\newline
(D)
24
−
4
ln
(
3
)
24-4 \ln (3)
24
−
4
ln
(
3
)
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Simplify. Express your answer using positive exponents.
\newline
(
2
v
3
)
(
4
v
)
(
5
v
)
(2v^3)(4v)(5v)
(
2
v
3
)
(
4
v
)
(
5
v
)
\newline
______
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