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Math Problems
Grade 8
Evaluate expressions using properties of exponents
Simplify by adding, subtracting, multiplying, or dividing, as indicated:
\newline
$
43.60
÷
20
\$43.60\div20
$43.60
÷
20
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Find all the factor pairs for
18
18
18
and complete the equations.
\newline
18
=
1
×
_
_
18 = 1 \times \_\_
18
=
1
×
__
\newline
18
=
_
_
×
9
18 = \_\_ \times 9
18
=
__
×
9
\newline
18
=
3
×
_
_
18 = 3 \times \_\_
18
=
3
×
__
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Find all the factor pairs for
20
20
20
and complete the equations.
\newline
20
=
_
_
_
×
20
20 = \_\_\_ \times 20
20
=
___
×
20
\newline
20
=
2
×
_
_
_
20 = 2 \times \_\_\_
20
=
2
×
___
\newline
20
=
_
_
_
×
5
20 = \_\_\_ \times 5
20
=
___
×
5
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Find all the factor pairs for
45
45
45
and complete the equations.
\newline
45
=
_
_
_
×
45
45 = \_\_\_ \times 45
45
=
___
×
45
\newline
45
=
3
×
_
_
_
45 = 3 \times \_\_\_
45
=
3
×
___
\newline
45
=
5
×
_
_
_
45 = 5 \times \_\_\_
45
=
5
×
___
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Use the model to find the product.
\newline
1
3
×
1
5
=
‾
/
‾
\frac{1}{3} \times \frac{1}{5} = \underline{\hspace{1cm}}/\underline{\hspace{1cm}}
3
1
×
5
1
=
/
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Use the model to find the product.
\newline
1
3
×
1
2
=
\frac{1}{3} \times \frac{1}{2} =
3
1
×
2
1
=
‾
\underline{\hspace{1cm}}
/
‾
\underline{\hspace{1cm}}
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Use the model to find the product.
\newline
1
4
×
1
5
=
‾
/
‾
\frac{1}{4} \times \frac{1}{5} = \underline{\hspace{1cm}}/\underline{\hspace{1cm}}
4
1
×
5
1
=
/
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Use the model to find the product.
\newline
1
2
×
1
5
=
‾
/
‾
\frac{1}{2} \times \frac{1}{5} = \underline{\hspace{1cm}}/\underline{\hspace{1cm}}
2
1
×
5
1
=
/
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Use the model to find the product.
\newline
1
4
×
1
2
=
\frac{1}{4} \times \frac{1}{2} =
4
1
×
2
1
=
‾
\underline{\hspace{1cm}}
/
‾
\underline{\hspace{1cm}}
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Use the model to find the product.
\newline
1
4
×
1
3
=
\frac{1}{4} \times \frac{1}{3} =
4
1
×
3
1
=
‾
\underline{\hspace{1cm}}
/
‾
\underline{\hspace{1cm}}
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Use the model to find the product.
\newline
1
3
×
1
3
=
\frac{1}{3} \times \frac{1}{3} =
3
1
×
3
1
=
‾
\underline{\hspace{1cm}}
/
‾
\underline{\hspace{1cm}}
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Use the model to find the product.
\newline
1
5
×
1
2
=
‾
/
‾
\frac{1}{5} \times \frac{1}{2} = \underline{\hspace{1cm}}/\underline{\hspace{1cm}}
5
1
×
2
1
=
/
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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
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
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
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
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
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
57
1
4
57
1
7
\frac{571^4}{571^7}
57
1
7
57
1
4
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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
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
+
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
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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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
(
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
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
Get tutor help
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
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
Get tutor help
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
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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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
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
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
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
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
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
9
n
9^{n}
9
n
.
\newline
(
9
−
3
)
(
9
12
)
=
(9^{-3})(9^{12})=
(
9
−
3
)
(
9
12
)
=
Get tutor help
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