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Math Problems
Grade 8
Evaluate expressions using properties of exponents
Simplify. Express your answer as a single term using exponents.
\newline
89
3
4
89
3
3
\frac{893^4}{893^3}
89
3
3
89
3
4
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Simplify. Express your answer as a single term using exponents.
\newline
53
1
3
53
1
5
\frac{531^3}{531^5}
53
1
5
53
1
3
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Simplify. Express your answer as a single term using exponents.
\newline
51
7
7
51
7
7
\frac{517^7}{517^7}
51
7
7
51
7
7
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Simplify. Express your answer as a single term using exponents.
\newline
63
6
2
63
6
9
\frac{636^2}{636^9}
63
6
9
63
6
2
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Simplify. Express your answer as a single term using exponents.
\newline
76
6
6
76
6
9
\frac{766^6}{766^9}
76
6
9
76
6
6
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Simplify. Express your answer as a single term using exponents.
\newline
95
8
2
95
8
3
\frac{958^2}{958^3}
95
8
3
95
8
2
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Simplify. Express your answer as a single term using exponents.
\newline
43
2
6
43
2
7
\frac{432^6}{432^7}
43
2
7
43
2
6
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Simplify. Express your answer as a single term using exponents.
\newline
52
8
2
52
8
3
\frac{528^2}{528^3}
52
8
3
52
8
2
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Simplify. Express your answer as a single term using exponents.
\newline
76
7
6
76
7
6
\frac{767^6}{767^6}
76
7
6
76
7
6
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Simplify. Express your answer as a single term using exponents.
\newline
57
1
4
57
1
7
\frac{571^4}{571^7}
57
1
7
57
1
4
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or each table, determine whether it shows that
x
x
x
and
y
y
y
are proportional.
\newline
x
x
x
and
y
y
y
are proportional, fill in the blank with a number in simplest form.
\newline
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\newline
\hline \multicolumn{
5
5
5
}{|c|}{ Table
1
1
1
} & \multicolumn{
5
5
5
}{|c|}{ Table
2
2
2
} \\
\newline
\hline
x
x
x
&
15
15
15
&
36
36
36
&
63
63
63
&
96
96
96
&
x
x
x
&
15
15
15
&
30
30
30
&
45
45
45
&
60
60
60
\\
\newline
\hline
y
y
y
&
3
3
3
&
6
6
6
&
9
9
9
&
12
12
12
&
y
y
y
&
6
6
6
&
12
12
12
&
18
18
18
&
24
24
24
\\
\newline
\hline \multicolumn{
5
5
5
}{|c|}{ Proportional } & \multicolumn{
5
5
5
}{|c|}{ Proportional } \\
\newline
\hline \multicolumn{
5
5
5
}{|c|}{
y
y
y
is
□
\square
□
times
x
x
x
} & \multicolumn{
5
5
5
}{|c|}{
y
y
y
is
□
\square
□
times
x
x
x
} \\
\newline
\hline \multicolumn{
5
5
5
}{|c|}{ Not proportional } & \multicolumn{
5
5
5
}{|c|}{ Not proportional } \\
\newline
\hline
\newline
\end{tabular}
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Simplify. Write your answer using whole numbers and variables.
\newline
h
2
+
h
24
h
\frac{h^2+h}{24h}
24
h
h
2
+
h
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Simplify. Write your answer using whole numbers and variables.
\newline
g
2
+
8
g
18
g
\frac{g^2 + 8g}{18g}
18
g
g
2
+
8
g
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Simplify. Write your answer using whole numbers and variables.
\newline
g
2
+
5
g
g
+
5
\frac{g^2 + 5g}{g + 5}
g
+
5
g
2
+
5
g
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Simplify. Write your answer using whole numbers and variables.
\newline
j
2
+
9
j
j
+
9
\frac{j^2 + 9j}{j + 9}
j
+
9
j
2
+
9
j
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Simplify. Write your answer using whole numbers and variables.
\newline
g
2
−
5
g
g
\frac{g^2 - 5g}{g}
g
g
2
−
5
g
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3
x
2
+
5
x
+
4
=
0
3x^2 +5x + 4 =0
3
x
2
+
5
x
+
4
=
0
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4
x
2
+
72
x
+
320
=
0
4x^2+72x+320=0
4
x
2
+
72
x
+
320
=
0
from least to greatest
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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
\mathbf{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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Simplify.
\newline
Rewrite the expression in the form
9
n
9^{n}
9
n
.
\newline
9
−
3
9
12
=
□
\frac{9^{-3}}{9^{12}}=\square
9
12
9
−
3
=
□
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Which expressions are equivalent to
\newline
7
−
2
⋅
7
6
7^{-2} \cdot 7^{6}
7
−
2
⋅
7
6
?
\newline
Choose
\newline
2
2
2
answers:
\newline
A
\newline
7
2
7
−
2
\frac{7^{2}}{7^{-2}}
7
−
2
7
2
\newline
B
\newline
7
6
7
−
2
\frac{7^{6}}{7^{-2}}
7
−
2
7
6
\newline
C
\newline
7
−
12
7^{-12}
7
−
12
\newline
D
\newline
(
7
2
)
2
(7^{2})^{2}
(
7
2
)
2
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Which expressions are equivalent to
\newline
5
12
⋅
5
8
5^{12} \cdot 5^{8}
5
12
⋅
5
8
?
\newline
Choose
2
2
2
answers:
\newline
A
\newline
2
5
20
25^{20}
2
5
20
\newline
B
\newline
(
2
5
5
)
4
(25^{5})^{4}
(
2
5
5
)
4
\newline
C.
\newline
(
5
3
⋅
5
2
)
4
(5^{3} \cdot 5^{2})^{4}
(
5
3
⋅
5
2
)
4
\newline
D
\newline
(
5
5
)
4
(5^{5})^{4}
(
5
5
)
4
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Which expressions are equivalent to
\newline
(
1
5
)
⋅
(
1
5
)
⋅
(
1
5
)
⋅
(
1
5
)
(\frac{1}{5})\cdot(\frac{1}{5})\cdot(\frac{1}{5})\cdot(\frac{1}{5})
(
5
1
)
⋅
(
5
1
)
⋅
(
5
1
)
⋅
(
5
1
)
?
\newline
Choose
2
2
2
answers:
\newline
A.
(
5
−
2
)
2
(5^{-2})^{2}
(
5
−
2
)
2
\newline
B.
(
5
−
4
)
0
(5^{-4})^{0}
(
5
−
4
)
0
\newline
C.
5
1
5
4
\frac{5^{1}}{5^{4}}
5
4
5
1
\newline
D.
5
2
⋅
5
−
6
5^{2}\cdot5^{-6}
5
2
⋅
5
−
6
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Which expressions are equivalent to
\newline
4
−
2
⋅
7
−
2
4^{-2} \cdot 7^{-2}
4
−
2
⋅
7
−
2
?
\newline
Choose
2
2
2
answers:
\newline
A)
\newline
(
4
⋅
7
)
−
4
(4 \cdot 7)^{-4}
(
4
⋅
7
)
−
4
\newline
B)
\newline
1
2
8
2
\frac{1}{28^{2}}
2
8
2
1
\newline
C)
\newline
7
−
2
4
2
\frac{7^{-2}}{4^{2}}
4
2
7
−
2
\newline
D)
\newline
(
4
⋅
7
)
4
(4 \cdot 7)^{4}
(
4
⋅
7
)
4
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Which expressions are equivalent to
\newline
7
×
7
×
7
×
7
×
7
×
7
7 \times 7 \times 7 \times 7 \times 7 \times 7
7
×
7
×
7
×
7
×
7
×
7
?
\newline
Choose
\newline
2
2
2
answers:
\newline
A
\newline
7
8
7
2
\frac{7^{8}}{7^{2}}
7
2
7
8
\newline
B
\newline
7
6
×
7
1
7^{6} \times 7^{1}
7
6
×
7
1
\newline
C
\newline
(
7
2
)
3
(7^{2})^{3}
(
7
2
)
3
\newline
D
\newline
7
12
7
2
\frac{7^{12}}{7^{2}}
7
2
7
12
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Which expressions are equivalent to
\newline
6
×
6
×
6
×
6
×
6
6 \times 6 \times 6 \times 6 \times 6
6
×
6
×
6
×
6
×
6
?
\newline
Choose
2
2
2
answers:
\newline
A)
(
6
2
)
3
(6^{2})^{3}
(
6
2
)
3
\newline
B)
2
5
×
3
5
2^{5} \times 3^{5}
2
5
×
3
5
\newline
C)
6
6
6
1
\frac{6^{6}}{6^{1}}
6
1
6
6
\newline
D)
3
2
×
2
3
3^{2} \times 2^{3}
3
2
×
2
3
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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
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
8
n
8^{n}
8
n
.
\newline
(
8
−
8
)
(
8
3
)
=
(8^{-8})(8^{3})=
(
8
−
8
)
(
8
3
)
=
Get tutor help
Select the equivalent expression.
\newline
(
6
−
4
⋅
8
−
7
)
−
9
=
(6^{-4}\cdot8^{-7})^{-9}=
(
6
−
4
⋅
8
−
7
)
−
9
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
6
13
⋅
8
16
\frac{1}{6^{13}\cdot8^{16}}
6
13
⋅
8
16
1
\newline
(B)
6
36
⋅
8
63
6^{36}\cdot8^{63}
6
36
⋅
8
63
\newline
(C)
6
5
⋅
8
2
6^{5}\cdot8^{2}
6
5
⋅
8
2
Get tutor help
Select the equivalent expression.
\newline
(
3
6
y
−
5
)
2
=
?
\left(\frac{3^{6}}{y^{-5}}\right)^{2}=\,?
(
y
−
5
3
6
)
2
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
6
y
−
10
\frac{3^{6}}{y^{-10}}
y
−
10
3
6
\newline
(B)
3
12
y
10
3^{12}y^{10}
3
12
y
10
\newline
(C)
3
12
y
−
5
\frac{3^{12}}{y^{-5}}
y
−
5
3
12
Get tutor help
Select the equivalent expression.
\newline
(
2
−
7
⋅
5
5
)
2
=
(2^{-7}\cdot5^{5})^{2}=
(
2
−
7
⋅
5
5
)
2
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
−
14
⋅
5
10
2^{-14}\cdot5^{10}
2
−
14
⋅
5
10
\newline
(B)
2
−
5
⋅
5
7
2^{-5}\cdot5^{7}
2
−
5
⋅
5
7
\newline
(C)
2
−
7
⋅
5
10
2^{-7}\cdot5^{10}
2
−
7
⋅
5
10
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
4
n
4^{n}
4
n
.
\newline
4
11
4
−
8
=
\frac{4^{11}}{4^{-8}}=
4
−
8
4
11
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
x
(
n
)
.
x^{(n)}.
x
(
n
)
.
\newline
x
(
2
)
⋅
x
(
−
12
)
=
x^{(2)}\cdot x^{(-12)}=
x
(
2
)
⋅
x
(
−
12
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
5
n
5^{n}
5
n
.
\newline
(
5
−
8
)
(
5
−
10
)
=
(5^{-8})(5^{-10})=
(
5
−
8
)
(
5
−
10
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
4
n
4^{n}
4
n
.
\newline
(
4
6
)
(
4
−
8
)
=
(4^{6})(4^{-8})=
(
4
6
)
(
4
−
8
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
4
n
4^{n}
4
n
.
\newline
(
4
11
)
(
4
−
8
)
=
(4^{11})(4^{-8})=
(
4
11
)
(
4
−
8
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
b
n
b^{n}
b
n
.
\newline
b
−
6
⋅
b
11
=
b^{-6} \cdot b^{11}=
b
−
6
⋅
b
11
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
z
n
z^{n}
z
n
.
\newline
z
−
11
⋅
z
−
15
z^{-11} \cdot z^{-15}
z
−
11
⋅
z
−
15
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
y
(
n
)
.
y^{(n)}.
y
(
n
)
.
\newline
y
(
−
4
)
⋅
y
(
3
)
=
y^{(-4)} \cdot y^{(3)} =
y
(
−
4
)
⋅
y
(
3
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
5
n
5^{n}
5
n
.
\newline
5
10
5
12
=
\frac{5^{10}}{5^{12}}=
5
12
5
10
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
6
n
6^{n}
6
n
.
\newline
6
−
6
6
−
5
=
\frac{6^{-6}}{6^{-5}}=
6
−
5
6
−
6
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
b
n
b^{n}
b
n
.
\newline
b
−
2
b
4
\frac{b^{-2}}{b^{4}}
b
4
b
−
2
=
Get tutor help
Select the equivalent expression.
\newline
(
z
4
6
2
)
−
3
=
\left(\frac{z^{4}}{6^{2}}\right)^{-3}=
(
6
2
z
4
)
−
3
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
z
6
−
1
\frac{z}{6^{-1}}
6
−
1
z
\newline
(B)
z
12
⋅
6
6
z^{12}\cdot 6^{6}
z
12
⋅
6
6
\newline
(C)
6
6
z
12
\frac{6^{6}}{z^{12}}
z
12
6
6
Get tutor help
Select the equivalent expression.
\newline
(
9
6
⋅
7
−
9
)
−
4
=
(9^{6}\cdot7^{-9})^{-4}=
(
9
6
⋅
7
−
9
)
−
4
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
24
7
36
\frac{9^{24}}{7^{36}}
7
36
9
24
\newline
(B)
7
36
9
24
\frac{7^{36}}{9^{24}}
9
24
7
36
\newline
(C)
9
24
⋅
7
−
36
9^{24}\cdot7^{-36}
9
24
⋅
7
−
36
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
a
n
a^{n}
a
n
.
\newline
a
5
⋅
a
−
3
=
a^{5} \cdot a^{-3} =
a
5
⋅
a
−
3
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
x
n
x^{n}
x
n
.
\newline
x
6
x
8
=
\frac{x^{6}}{x^{8}}=
x
8
x
6
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
z
n
z^{n}
z
n
.
\newline
z
7
z
−
14
\frac{z^{7}}{z^{-14}}
z
−
14
z
7
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
9
n
9^{n}
9
n
.
\newline
(
9
−
3
)
(
9
12
)
=
(9^{-3})(9^{12})=
(
9
−
3
)
(
9
12
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
y
n
y^{n}
y
n
.
\newline
y
−
7
y
−
13
\frac{y^{-7}}{y^{-13}}
y
−
13
y
−
7
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
a
n
a^{n}
a
n
.
\newline
a
−
13
a
−
6
=
\frac{a^{-13}}{a^{-6}}=
a
−
6
a
−
13
=
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