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Math Problems
Grade 8
Negative Exponents
Which sign makes the statement true?
\newline
10
14
?
5
6
\frac{10}{14} ? \frac{5}{6}
14
10
?
6
5
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
Get tutor help
Which sign makes the statement true?
\newline
−
1
3
?
−
3
12
-\frac{1}{3} ? -\frac{3}{12}
−
3
1
?
−
12
3
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
Get tutor help
Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
4
)
0
=
(\frac{1}{4})^0 =
(
4
1
)
0
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
3
4
)
0
(\frac{3}{4})^0
(
4
3
)
0
=
_
_
_
_
\_\_\_\_
____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
2
3
)
1
=
(\frac{2}{3})^1 =
(
3
2
)
1
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
3
)
1
=
(\frac{1}{3})^1 =
(
3
1
)
1
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
2
)
1
=
(\frac{1}{2})^1 =
(
2
1
)
1
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
2
3
)
0
=
(\frac{2}{3})^0 =
(
3
2
)
0
=
_
_
_
_
\_\_\_\_
____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
3
4
)
1
=
(\frac{3}{4})^1 =
(
4
3
)
1
=
_____
Get tutor help
Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
3
)
0
(\frac{1}{3})^0
(
3
1
)
0
=
_
_
_
_
\_\_\_\_
____
Get tutor help
Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
4
)
1
=
(\frac{1}{4})^1 =
(
4
1
)
1
=
_____
Get tutor help
Evaluate. Write your answer as a fraction or whole number.
\newline
(
2
3
)
2
=
(\frac{2}{3})^{2}=
(
3
2
)
2
=
\newline
□
\square
□
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Identify whether the equation below has one solution, no solutions or an infinite number of solutions. Explain your answer.
\newline
3
(
4
x
−
5
)
=
6
x
+
15
3(4 x-5)=6 x+15
3
(
4
x
−
5
)
=
6
x
+
15
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Simplify:
(
x
+
1
)
2
−
7
(x+1)^2-7
(
x
+
1
)
2
−
7
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The product of two numbers is the greatest
2
2
2
-digit number. If one of the numbers is
−
11
-11
−
11
, find the other number.
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Which is equal to
7
−
7
7^{-7}
7
−
7
?
\newline
Choices:
\newline
(A)
1
7
7
\frac{1}{7^7}
7
7
1
\newline
(B)
−
(
−
7
)
7
-(-7)^7
−
(
−
7
)
7
\newline
(C)
1
(
−
7
)
7
\frac{1}{(-7)^7}
(
−
7
)
7
1
\newline
(D)
−
1
(
−
7
)
−
7
-\frac{1}{(-7)^{-7}}
−
(
−
7
)
−
7
1
Get tutor help
Which is equal to
5
−
8
5^{-8}
5
−
8
?
\newline
Choices:
\newline
(A)
−
(
−
5
)
8
-(-5)^8
−
(
−
5
)
8
\newline
(B)
(
−
5
)
8
(-5)^8
(
−
5
)
8
\newline
(C)
1
5
8
\frac{1}{5^8}
5
8
1
\newline
(D)
−
1
5
−
8
-\frac{1}{5^{-8}}
−
5
−
8
1
Get tutor help
Which is equal to
1
4
5
\frac{1}{4^5}
4
5
1
?
\newline
Choices:
\newline
(A)
−
1
(
−
4
)
−
5
-\frac{1}{(-4)^{-5}}
−
(
−
4
)
−
5
1
\newline
(B)
1
(
−
4
)
5
\frac{1}{(-4)^5}
(
−
4
)
5
1
\newline
(C)
1
4
−
5
\frac{1}{4^{-5}}
4
−
5
1
\newline
(D)
4
−
5
4^{-5}
4
−
5
Get tutor help
Which is equal to
1
9
2
\frac{1}{9^2}
9
2
1
?
\newline
Choices:
\newline
(A)
−
(
−
9
)
2
-(-9)^2
−
(
−
9
)
2
\newline
(B)
9
−
2
9^{-2}
9
−
2
\newline
(C)
−
9
2
-9^2
−
9
2
\newline
(D)
−
1
9
−
2
-\frac{1}{9^{-2}}
−
9
−
2
1
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Which is equal to
1
8
5
\frac{1}{8^5}
8
5
1
?
\newline
Choices:
\newline
(A)
−
8
5
-8^5
−
8
5
\newline
(B)
8
−
5
8^{-5}
8
−
5
\newline
(C)
(
−
8
)
−
5
(-8)^{-5}
(
−
8
)
−
5
\newline
(D)
−
1
8
−
5
-\frac{1}{8^{-5}}
−
8
−
5
1
Get tutor help
Which is equal to
1
5
9
\frac{1}{5^9}
5
9
1
?
\newline
Choices:
\newline
(A)
5
−
9
5^{-9}
5
−
9
\newline
(B)
(
−
5
)
9
(-5)^9
(
−
5
)
9
\newline
(C)
1
5
−
9
\frac{1}{5^{-9}}
5
−
9
1
\newline
(D)
5
9
5^9
5
9
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Which is equal to
1
7
6
\frac{1}{7^6}
7
6
1
?
\newline
Choices:
\newline
(A)
7
−
6
7^{-6}
7
−
6
\newline
(B)
−
7
6
-7^6
−
7
6
\newline
(C)
−
1
7
−
6
-\frac{1}{7^{-6}}
−
7
−
6
1
\newline
(D)
(
−
7
)
6
(-7)^6
(
−
7
)
6
Get tutor help
Which is equal to
1
8
7
\frac{1}{8^7}
8
7
1
?
\newline
Choices:
\newline
(A)
8
−
7
8^{-7}
8
−
7
\newline
(B)
(
−
8
)
7
(-8)^7
(
−
8
)
7
\newline
(C)
1
(
−
8
)
7
\frac{1}{(-8)^7}
(
−
8
)
7
1
\newline
(D)
−
(
−
8
)
7
-(-8)^7
−
(
−
8
)
7
Get tutor help
Which is equal to
2
−
9
2^{-9}
2
−
9
?
\newline
Choices:
\newline
(A)
1
2
9
\frac{1}{2^9}
2
9
1
\newline
(B)
2
9
2^9
2
9
\newline
(C)
1
(
−
2
)
9
\frac{1}{(-2)^9}
(
−
2
)
9
1
\newline
(D)
1
(
−
2
)
−
9
\frac{1}{(-2)^{-9}}
(
−
2
)
−
9
1
Get tutor help
Which is equal to
1
3
4
\frac{1}{3^4}
3
4
1
?
\newline
Choices:
\newline
(A)
3
4
3^4
3
4
\newline
(B)
−
1
3
−
4
-\frac{1}{3^{-4}}
−
3
−
4
1
\newline
(C)
3
−
4
3^{-4}
3
−
4
\newline
(D)
−
(
−
3
)
4
-(-3)^4
−
(
−
3
)
4
Get tutor help
Which is equal to
3
−
7
3^{-7}
3
−
7
?
\newline
Choices:
\newline
(A)
(
−
3
)
−
7
(-3)^{-7}
(
−
3
)
−
7
\newline
(B)
3
7
3^{7}
3
7
\newline
(C)
−
1
3
−
7
-\frac{1}{3^{-7}}
−
3
−
7
1
\newline
(D)
1
3
7
\frac{1}{3^{7}}
3
7
1
Get tutor help
Which is equal to
1
8
2
\frac{1}{8^2}
8
2
1
?
\newline
Choices:
\newline
(A)
−
1
8
−
2
-\frac{1}{8^{-2}}
−
8
−
2
1
\newline
(B)
8
−
2
8^{-2}
8
−
2
\newline
(C)
1
8
−
2
\frac{1}{8^{-2}}
8
−
2
1
\newline
(D)
−
1
(
−
8
)
−
2
-\frac{1}{(-8)^{-2}}
−
(
−
8
)
−
2
1
Get tutor help
Which is equal to
1
2
3
\frac{1}{2^3}
2
3
1
?
\newline
Choices:
\newline
(A)
2
3
2^3
2
3
\newline
(B)
2
−
3
2^{-3}
2
−
3
\newline
(C)
(
−
2
)
3
(-2)^3
(
−
2
)
3
\newline
(D)
−
(
−
2
)
3
-(-2)^3
−
(
−
2
)
3
Get tutor help
Which is equal to
4
−
3
4^{-3}
4
−
3
?
\newline
Choices:
\newline
(A)
−
(
−
4
)
3
-(-4)^3
−
(
−
4
)
3
\newline
(B)
1
4
3
\frac{1}{4^3}
4
3
1
\newline
(C)
(
−
4
)
−
3
(-4)^{-3}
(
−
4
)
−
3
\newline
(D)
4
3
4^3
4
3
Get tutor help
Which is equal to
1
7
9
\frac{1}{7^9}
7
9
1
?
\newline
Choices:
\newline
(A)
−
1
(
−
7
)
−
9
-\frac{1}{(-7)^{-9}}
−
(
−
7
)
−
9
1
\newline
(B)
1
(
−
7
)
9
\frac{1}{(-7)^9}
(
−
7
)
9
1
\newline
(C)
(
−
7
)
9
(-7)^9
(
−
7
)
9
\newline
(D)
7
−
9
7^{-9}
7
−
9
Get tutor help
Which is equal to
1
2
5
\frac{1}{2^5}
2
5
1
?
\newline
Choices:
\newline
(A)
−
2
5
-2^5
−
2
5
\newline
(B)
−
(
−
2
)
5
-(-2)^5
−
(
−
2
)
5
\newline
(C)
(
−
2
)
−
5
(-2)^{-5}
(
−
2
)
−
5
\newline
(D)
2
−
5
2^{-5}
2
−
5
Get tutor help
Which is equal to
3
−
2
3^{-2}
3
−
2
?
\newline
Choices:
\newline
(A)
−
(
−
3
)
2
-(-3)^2
−
(
−
3
)
2
\newline
(B)
1
3
2
\frac{1}{3^2}
3
2
1
\newline
(C)
1
3
−
2
\frac{1}{3^{-2}}
3
−
2
1
\newline
(D)
3
2
3^2
3
2
Get tutor help
Which is equal to
8
−
3
8^{-3}
8
−
3
?
\newline
Choices:
\newline
(A)
−
8
3
-8^3
−
8
3
\newline
(B)
1
8
3
\frac{1}{8^3}
8
3
1
\newline
(C)
−
1
(
−
8
)
−
3
-\frac{1}{(-8)^{-3}}
−
(
−
8
)
−
3
1
\newline
(D)
−
1
8
−
3
-\frac{1}{8^{-3}}
−
8
−
3
1
Get tutor help
Which is equal to
6
−
3
6^{-3}
6
−
3
?
\newline
Choices:
\newline
(A)
6
3
6^3
6
3
\newline
(B)
1
6
3
\frac{1}{6^3}
6
3
1
\newline
(C)
(
−
6
)
−
3
(-6)^{-3}
(
−
6
)
−
3
\newline
(D)
−
1
6
−
3
-\frac{1}{6^{-3}}
−
6
−
3
1
Get tutor help
Which is equal to
1
2
7
\frac{1}{2^7}
2
7
1
?
\newline
Choices:
\newline
(A)
2
−
7
2^{-7}
2
−
7
\newline
(B)
−
1
(
−
2
)
−
7
-\frac{1}{(-2)^{-7}}
−
(
−
2
)
−
7
1
\newline
(C)
1
2
−
7
\frac{1}{2^{-7}}
2
−
7
1
\newline
(D)
(
−
2
)
7
(-2)^7
(
−
2
)
7
Get tutor help
Which is equal to
1
4
7
\frac{1}{4^7}
4
7
1
?
\newline
Choices:
\newline
(A)
4
−
7
4^{-7}
4
−
7
\newline
(B)
−
1
4
−
7
-\frac{1}{4^{-7}}
−
4
−
7
1
\newline
(C)
−
4
7
-4^7
−
4
7
\newline
(D)
1
(
−
4
)
7
\frac{1}{(-4)^7}
(
−
4
)
7
1
Get tutor help
Which is equal to
6
−
5
6^{-5}
6
−
5
?
\newline
Choices:
\newline
(A)
−
6
5
-6^5
−
6
5
\newline
(B)
1
6
5
\frac{1}{6^5}
6
5
1
\newline
(C)
6
5
6^5
6
5
\newline
(D)
1
(
−
6
)
−
5
\frac{1}{(-6)^{-5}}
(
−
6
)
−
5
1
Get tutor help
Which is equal to
7
−
2
7^{-2}
7
−
2
?
\newline
Choices:
\newline
(A)
−
(
−
7
)
2
-(-7)^2
−
(
−
7
)
2
\newline
(B)
1
7
2
\frac{1}{7^2}
7
2
1
\newline
(C)
−
1
(
−
7
)
−
2
-\frac{1}{(-7)^{-2}}
−
(
−
7
)
−
2
1
\newline
(D)
−
1
7
−
2
-\frac{1}{7^{-2}}
−
7
−
2
1
Get tutor help
Which is equal to
1
4
7
\frac{1}{4^7}
4
7
1
?
\newline
Choices:
\newline
(A)
4
−
7
4^{-7}
4
−
7
\newline
(B)
1
(
−
4
)
7
\frac{1}{(-4)^7}
(
−
4
)
7
1
\newline
(C)
−
1
(
−
4
)
−
7
-\frac{1}{(-4)^{-7}}
−
(
−
4
)
−
7
1
\newline
(D)
−
1
4
−
7
-\frac{1}{4^{-7}}
−
4
−
7
1
Get tutor help
Which is equal to
1
4
6
\frac{1}{4^6}
4
6
1
?
\newline
Choices:
\newline
(A)
1
4
−
6
\frac{1}{4^{-6}}
4
−
6
1
\newline
(B)
4
6
4^6
4
6
\newline
(C)
−
(
−
4
)
6
-(-4)^6
−
(
−
4
)
6
\newline
(D)
4
−
6
4^{-6}
4
−
6
Get tutor help
Which is equal to
9
−
4
9^{-4}
9
−
4
?
\newline
Choices:
\newline
(A)
−
9
4
-9^4
−
9
4
\newline
(B)
1
9
4
\frac{1}{9^4}
9
4
1
\newline
(C)
−
1
(
−
9
)
−
4
\frac{-1}{(-9)^{-4}}
(
−
9
)
−
4
−
1
\newline
(D)
1
(
−
9
)
−
4
\frac{1}{(-9)^{-4}}
(
−
9
)
−
4
1
Get tutor help
Which is equal to
5
−
8
5^{-8}
5
−
8
?
\newline
Choices:
\newline
(A)
1
5
8
\frac{1}{5^8}
5
8
1
\newline
(B)
(
−
5
)
8
(-5)^8
(
−
5
)
8
\newline
(C)
−
1
5
−
8
-\frac{1}{5^{-8}}
−
5
−
8
1
\newline
(D)
−
5
8
-5^8
−
5
8
Get tutor help
Which is equal to
1
6
6
\frac{1}{6^6}
6
6
1
?
\newline
Choices:
\newline
(A)
6
−
6
6^{-6}
6
−
6
\newline
(B)
(
−
6
)
6
(-6)^6
(
−
6
)
6
\newline
(C)
1
6
−
6
\frac{1}{6^{-6}}
6
−
6
1
\newline
(D)
−
1
(
−
6
)
−
6
-\frac{1}{(-6)^{-6}}
−
(
−
6
)
−
6
1
Get tutor help
Evaluate and simplify the following complex fraction.
\newline
6
−
7
3
11
=
\frac{\frac{6}{-7}}{\frac{3}{11}}=
11
3
−
7
6
=
Get tutor help
Evaluate and simplify the following complex fraction.
\newline
9
−
5
−
3
8
=
\frac{\frac{9}{-5}}{\frac{-3}{8}}=
8
−
3
−
5
9
=
Get tutor help
Evaluate and simplify the following complex fraction.
\newline
2
3
4
−
9
=
□
\frac{\frac{2}{3}}{\frac{4}{-9}}=\square
−
9
4
3
2
=
□
Get tutor help
Evaluate and simplify the following complex fraction.
\newline
−
5
7
2
4
=
□
\frac{\frac{-5}{7}}{\frac{2}{4}}=\square
4
2
7
−
5
=
□
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Evaluate and simplify the following complex fraction.
\newline
−
2
−
7
4
−
9
=
□
\frac{\frac{-2}{-7}}{\frac{4}{-9}}=\square
−
9
4
−
7
−
2
=
□
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Evaluate and simplify the following complex fraction.
\newline
3
8
1
−
7
=
□
\frac{\frac{3}{8}}{\frac{1}{-7}}=\square
−
7
1
8
3
=
□
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Find the area of a circle with a circumference of
37
37
37
.
68
68
68
units.
\newline
□
\square
□
units
2
^{2}
2
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1
2
3
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