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Math Problems
Grade 8
Multiply and divide powers: variable bases
Simplify. Write your answer using whole numbers and variables.
\newline
8
w
2
+
7
w
w
\frac{8w^2 + 7w}{w}
w
8
w
2
+
7
w
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Simplify. Write your answer using whole numbers and variables.
\newline
8
d
2
+
3
d
d
\frac{8d^2 + 3d}{d}
d
8
d
2
+
3
d
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Simplify. Write your answer using whole numbers and variables.
\newline
w
2
−
10
w
w
\frac{w^2 - 10w}{w}
w
w
2
−
10
w
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Simplify. Write your answer using whole numbers and variables.
\newline
z
−
8
z
2
−
8
z
\frac{z - 8}{z^2 - 8z}
z
2
−
8
z
z
−
8
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Simplify. Write your answer using whole numbers and variables.
\newline
r
2
−
5
r
r
−
5
\frac{r^2 - 5r}{r - 5}
r
−
5
r
2
−
5
r
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Simplify. Write your answer using whole numbers and variables.
\newline
d
2
−
3
d
d
−
3
\frac{d^2 - 3d}{d - 3}
d
−
3
d
2
−
3
d
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Simplify. Write your answer using whole numbers and variables.
\newline
2
k
2
+
9
k
2
k
+
9
\frac{2k^2 + 9k}{2k + 9}
2
k
+
9
2
k
2
+
9
k
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Simplify. Write your answer using whole numbers and variables.
\newline
7
r
2
−
8
r
7
r
−
8
\frac{7r^2 - 8r}{7r - 8}
7
r
−
8
7
r
2
−
8
r
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Simplify. Write your answer using whole numbers and variables.
\newline
5
d
2
−
8
d
5
d
−
8
\frac{5d^2 - 8d}{5d - 8}
5
d
−
8
5
d
2
−
8
d
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Simplify. Write your answer using whole numbers and variables.
\newline
2
r
2
+
5
r
2
r
+
5
\frac{2r^2 + 5r}{2r + 5}
2
r
+
5
2
r
2
+
5
r
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Simplify. Write your answer using whole numbers and variables.
\newline
5
y
2
−
3
y
5
y
−
3
\frac{5y^2 - 3y}{5y - 3}
5
y
−
3
5
y
2
−
3
y
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Simplify. Write your answer using whole numbers and variables.
\newline
9
z
2
−
8
z
9
z
−
8
\frac{9z^2 - 8z}{9z - 8}
9
z
−
8
9
z
2
−
8
z
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Simplify. Write your answer using whole numbers and variables.
\newline
m
−
10
m
2
−
10
m
\frac{m - 10}{m^2 - 10m}
m
2
−
10
m
m
−
10
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Simplify. Write your answer using whole numbers and variables.
\newline
5
y
2
−
2
y
5
y
−
2
\frac{5y^2 - 2y}{5y - 2}
5
y
−
2
5
y
2
−
2
y
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Simplify. Write your answer using whole numbers and variables.
\newline
w
+
7
w
2
+
7
w
\frac{w + 7}{w^2 + 7w}
w
2
+
7
w
w
+
7
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Simplify. Write your answer using whole numbers and variables.
\newline
n
−
10
n
2
−
10
n
\frac{n - 10}{n^2 - 10n}
n
2
−
10
n
n
−
10
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Simplify. Write your answer using whole numbers and variables.
\newline
w
−
8
w
2
−
8
w
\frac{w - 8}{w^2 - 8w}
w
2
−
8
w
w
−
8
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Simplify. Write your answer using whole numbers and variables.
\newline
7
j
2
−
10
j
7
j
−
10
\frac{7j^2 - 10j}{7j - 10}
7
j
−
10
7
j
2
−
10
j
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Simplify. Write your answer using whole numbers and variables.
\newline
7
j
2
−
5
j
7
j
−
5
\frac{7j^2 - 5j}{7j - 5}
7
j
−
5
7
j
2
−
5
j
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Simplify. Write your answer using whole numbers and variables.
\newline
8
p
2
−
7
p
8
p
−
7
\frac{8p^2 - 7p}{8p - 7}
8
p
−
7
8
p
2
−
7
p
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Simplify. Write your answer using whole numbers and variables.
\newline
7
q
2
−
3
q
7
q
−
3
\frac{7q^2 - 3q}{7q - 3}
7
q
−
3
7
q
2
−
3
q
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Simplify. Write your answer using whole numbers and variables.
\newline
4
s
2
−
7
s
4
s
−
7
\frac{4s^2 - 7s}{4s - 7}
4
s
−
7
4
s
2
−
7
s
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Simplify. Write your answer using whole numbers and variables.
\newline
u
−
6
u
2
−
6
u
\frac{u - 6}{u^2 - 6u}
u
2
−
6
u
u
−
6
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Determine the intervals where the function
f
(
x
)
=
x
3
−
3
x
2
+
2
x
x
2
−
2
x
+
1
f(x)=\frac{x^{3}-3x^{2}+2x}{x^{2}-2x+1}
f
(
x
)
=
x
2
−
2
x
+
1
x
3
−
3
x
2
+
2
x
is concave up or concave down.
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Simplify. Express your answer using positive exponents.
\newline
10
w
8
10
w
\frac{10w^8}{10w}
10
w
10
w
8
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Simplify. Express your answer using positive exponents.
\newline
8
y
8
y
\frac{8y}{8y}
8
y
8
y
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Simplify. Express your answer using positive exponents.
\newline
8
g
8
g
7
\frac{8g}{8g^7}
8
g
7
8
g
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Simplify. Express your answer using positive exponents.
\newline
9
k
9
k
\frac{9k}{9k}
9
k
9
k
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Simplify. Express your answer using positive exponents.
\newline
4
d
4
d
7
\frac{4d}{4d^7}
4
d
7
4
d
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Simplify. Express your answer using positive exponents.
\newline
5
c
5
c
\frac{5c}{5c}
5
c
5
c
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Simplify. Express your answer using positive exponents.
\newline
2
b
5
2
b
7
\frac{2b^5}{2b^7}
2
b
7
2
b
5
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Simplify. Express your answer using positive exponents.
\newline
2
v
2
2
v
7
\frac{2v^2}{2v^7}
2
v
7
2
v
2
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Simplify. Express your answer using positive exponents.
\newline
7
h
7
h
\frac{7h}{7h}
7
h
7
h
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Simplify. Express your answer using positive exponents.
\newline
5
y
5
y
3
\frac{5y}{5y^3}
5
y
3
5
y
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Simplify. Express your answer using positive exponents.
\newline
7
z
7
z
\frac{7z}{7z}
7
z
7
z
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Simplify. Express your answer using positive exponents.
\newline
5
y
5
y
4
\frac{5y}{5y^4}
5
y
4
5
y
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Simplify. Express your answer using positive exponents.
\newline
10
u
10
u
\frac{10u}{10u}
10
u
10
u
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Simplify. Express your answer using positive exponents.
\newline
3
g
5
3
g
5
\frac{3g^5}{3g^5}
3
g
5
3
g
5
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Simplify. Express your answer using positive exponents.
\newline
6
w
2
6
w
7
\frac{6w^2}{6w^7}
6
w
7
6
w
2
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Simplify. Express your answer using positive exponents.
\newline
6
u
6
u
8
\frac{6u}{6u^8}
6
u
8
6
u
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Simplify. Express your answer using positive exponents.
\newline
8
g
8
g
\frac{8g}{8g}
8
g
8
g
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Simplify. Express your answer using positive exponents.
\newline
8
w
8
w
\frac{8w}{8w}
8
w
8
w
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Which number represents the probability of an event that is an equal chance or
5
5
5
O
−
5
-5
−
5
O to occur?
\newline
39
20
\frac{39}{20}
20
39
\newline
0
0
0
\newline
1
2
\frac{1}{2}
2
1
\newline
1
1
1
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Simplify. Express your answer using positive exponents.
\newline
2
b
(
2
b
)
(
b
9
)
\frac{2b}{(2b)(b^9)}
(
2
b
)
(
b
9
)
2
b
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Simplify. Express your answer using positive exponents.
\newline
10
f
6
⋅
8
f
2
f
9
\frac{10f^6 \cdot 8f}{2f^9}
2
f
9
10
f
6
⋅
8
f
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Simplify. Express your answer using positive exponents.
\newline
(
9
k
4
)
(
7
k
4
)
(
5
k
8
)
(9k^4)(7k^4)(5k^8)
(
9
k
4
)
(
7
k
4
)
(
5
k
8
)
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Simplify. Express your answer using positive exponents.
\newline
(
8
m
4
)
(
5
m
)
(
4
m
)
(8m^4)(5m)(4m)
(
8
m
4
)
(
5
m
)
(
4
m
)
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Simplify. Express your answer using positive exponents.
\newline
8
a
7
(
4
a
6
)
(
a
5
)
\frac{8a^7}{(4a^6)(a^5)}
(
4
a
6
)
(
a
5
)
8
a
7
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Simplify. Express your answer using positive exponents.
\newline
(
2
k
9
)
(
10
k
8
)
(
9
k
2
)
(2k^9)(10k^8)(9k^2)
(
2
k
9
)
(
10
k
8
)
(
9
k
2
)
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Simplify. Express your answer using positive exponents.
\newline
8
d
2
2
d
⋅
d
2
\frac{8d^2}{2d \cdot d^2}
2
d
⋅
d
2
8
d
2
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