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Math Problems
Grade 8
Negative Exponents
Find the area of a circle with a diameter of
16
16
16
.
\newline
Either enter an exact answer in terms of
π
\pi
π
or use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
2
^{2}
2
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Find the area of a circle with a diameter of
6
6
6
.
\newline
Either enter an exact answer in terms of
π
\pi
π
or use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
2
^{2}
2
Get tutor help
Find the area of a circle with a radius of
3
3
3
.
\newline
Either enter an exact answer in terms of
π
\pi
π
or use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
2
^{2}
2
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Find the area of a circle with a radius of
2
2
2
.
\newline
Either enter an exact answer in terms of
π
\pi
π
or use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
2
^{2}
2
Get tutor help
Find the area of a circle with a radius of
8
8
8
.
\newline
Either enter an exact answer in terms of
π
\pi
π
or use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
2
^{2}
2
Get tutor help
Find the area of a circle with a circumference of
18
18
18
.
84
84
84
units.
\newline
□
\square
□
units
2
^{2}
2
Get tutor help
Find the area of a circle with a diameter of
4
4
4
.
\newline
Either enter an exact answer in terms of
π
\pi
π
or use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
2
^{2}
2
Get tutor help
Simplify.
\newline
9
×
(
−
4
)
=
9 \times(-4)=
9
×
(
−
4
)
=
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b
14
+
4
=
3
\frac{b}{14}+4=3
14
b
+
4
=
3
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−
5
(
3
x
−
10
)
=
5
-5(3x - 10) = 5
−
5
(
3
x
−
10
)
=
5
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Simplify. Write your answer using whole numbers and variables.
\newline
36
c
−
27
4
c
−
3
\frac{36c - 27}{4c - 3}
4
c
−
3
36
c
−
27
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y
=
4
(
x
+
3
)
2
−
8
y=4(x+3)^2-8
y
=
4
(
x
+
3
)
2
−
8
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∑
n
=
1
∞
n
+
1
n
!
\sum_{n=1}^{\infty} \frac{n+1}{n !}
n
=
1
∑
∞
n
!
n
+
1
\newline
Study if it converges or diverges using Ratio test.
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(
2
r
−
5
)
5
(2r-5)^5
(
2
r
−
5
)
5
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Perform the operation and express your answer as a single fraction in simplest form.
\newline
1
4
x
+
4
\frac{1}{4 x}+4
4
x
1
+
4
\newline
Answer:
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Solve for
x
x
x
.
\newline
−
2
x
−
5
5
x
−
3
+
6
x
−
16
6
−
10
x
=
−
1
2
\dfrac{-2x-5}{5x-3} + \dfrac{6x-16}{6-10x} = \dfrac{-1}{2}
5
x
−
3
−
2
x
−
5
+
6
−
10
x
6
x
−
16
=
2
−
1
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
2
)
2
=
(\frac{1}{2})^2 =
(
2
1
)
2
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
3
4
)
3
(\frac{3}{4})^3
(
4
3
)
3
=
_
_
\_\_
__
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Evaluate. Write your answer as a decimal or whole number.
\newline
(
0.01
)
4
=
(0.01)^4 =
(
0.01
)
4
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
3
)
3
=
(\frac{1}{3})^3 =
(
3
1
)
3
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
3
4
)
2
(\frac{3}{4})^2
(
4
3
)
2
=
_
_
\_\_
__
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
2
3
)
4
(\frac{2}{3})^4
(
3
2
)
4
= _____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
3
)
4
(\frac{1}{3})^4
(
3
1
)
4
=
_
_
\_\_
__
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
3
4
)
4
=
(\frac{3}{4})^4 =
(
4
3
)
4
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
2
)
4
=
(\frac{1}{2})^4 =
(
2
1
)
4
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
2
3
)
2
(\frac{2}{3})^2
(
3
2
)
2
=
_
_
\_\_
__
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
4
)
3
=
(\frac{1}{4})^3 =
(
4
1
)
3
=
_
_
_
_
\_\_\_\_
____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
4
)
2
=
(\frac{1}{4})^2 =
(
4
1
)
2
=
_____
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
3
)
2
(\frac{1}{3})^2
(
3
1
)
2
=
_
_
\_\_
__
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Evaluate. Write your answer as a fraction or whole number.
\newline
(
1
2
)
3
=
(\frac{1}{2})^3 =
(
2
1
)
3
=
_____
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Which is equal to
1
6
3
\frac{1}{6^3}
6
3
1
?
\newline
Choices:
\newline
(A)
−
6
3
-6^3
−
6
3
\newline
(B)
6
−
3
6^{-3}
6
−
3
\newline
(C)
(
−
6
)
−
3
(-6)^{-3}
(
−
6
)
−
3
\newline
(D)
−
1
(
−
6
)
−
3
-\frac{1}{(-6)^{-3}}
−
(
−
6
)
−
3
1
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Which is equal to
1
7
4
\frac{1}{7^4}
7
4
1
?
\newline
Choices:
\newline
(A)
−
7
4
-7^4
−
7
4
\newline
(B)
7
−
4
7^{-4}
7
−
4
\newline
(C)
−
1
7
−
4
-\frac{1}{7^{-4}}
−
7
−
4
1
\newline
(D)
−
(
−
7
)
4
-(-7)^4
−
(
−
7
)
4
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Which is equal to
1
4
7
\frac{1}{4^7}
4
7
1
?
\newline
Choices:
\newline
(A)
1
(
−
4
)
7
\frac{1}{(-4)^7}
(
−
4
)
7
1
\newline
(B)
1
(
−
4
)
−
7
\frac{1}{(-4)^{-7}}
(
−
4
)
−
7
1
\newline
(C)
4
−
7
4^{-7}
4
−
7
\newline
(D)
−
4
7
-4^7
−
4
7
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Which is equal to
1
4
6
\frac{1}{4^6}
4
6
1
?
\newline
Choices:
\newline
(A)
−
(
−
4
)
6
-(-4)^6
−
(
−
4
)
6
\newline
(B)
1
4
−
6
\frac{1}{4^{-6}}
4
−
6
1
\newline
(C)
−
4
6
-4^6
−
4
6
\newline
(D)
4
−
6
4^{-6}
4
−
6
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Which is equal to
1
7
5
\frac{1}{7^5}
7
5
1
?
\newline
Choices:
\newline
(A)
−
(
−
7
)
5
-(-7)^5
−
(
−
7
)
5
\newline
(B)
7
5
7^5
7
5
\newline
(C)
−
7
5
-7^5
−
7
5
\newline
(D)
7
−
5
7^{-5}
7
−
5
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Which is equal to
1
9
9
\frac{1}{9^9}
9
9
1
?
\newline
Choices:
\newline
(A)
9
−
9
9^{-9}
9
−
9
\newline
(B)
9
9
9^9
9
9
\newline
(C)
(
−
9
)
−
9
(-9)^{-9}
(
−
9
)
−
9
\newline
(D)
−
1
(
−
9
)
−
9
-\frac{1}{(-9)^{-9}}
−
(
−
9
)
−
9
1
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
2
×
1
6
\frac{1}{2} \times \frac{1}{6}
2
1
×
6
1
\newline
Answer:
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[
−
3
(
2
j
−
5
k
)
2
]
2
[-3(2j-5k)^2]^2
[
−
3
(
2
j
−
5
k
)
2
]
2
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[
−
3
(
2
j
−
5
k
2
)
]
2
[-3(2j-5k^2)]^2
[
−
3
(
2
j
−
5
k
2
)
]
2
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(
1
2
)
−
2
+
3
0
(\frac{1}{2})^{-2} + 3^{0}
(
2
1
)
−
2
+
3
0
Get tutor help
Evaluate.
\newline
(
5
−
2
)
(
4
)
÷
9
(5-2)^{(4)}\div 9
(
5
−
2
)
(
4
)
÷
9
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Solve for
x
\mathrm{x}
x
.
\newline
x
+
1
x
+
2
=
7
6
\frac{x+1}{x+2}=\frac{7}{6}
x
+
2
x
+
1
=
6
7
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
2
x
+
2
x
+
4
=
4
5
\frac{2 x+2}{x+4}=\frac{4}{5}
x
+
4
2
x
+
2
=
5
4
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
−
5
3
+
x
−
1
6
=
x
−
6
\frac{-5}{3}+\frac{x-1}{6}=x-6
3
−
5
+
6
x
−
1
=
x
−
6
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
−
4
3
+
3
x
+
7
12
=
1
\frac{-4}{3}+\frac{3 x+7}{12}=1
3
−
4
+
12
3
x
+
7
=
1
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
4
x
−
8
x
−
1
=
3
4
\frac{4 x-8}{x-1}=\frac{3}{4}
x
−
1
4
x
−
8
=
4
3
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
3
x
+
5
=
4
x
−
7
\frac{3}{x+5}=\frac{4}{x-7}
x
+
5
3
=
x
−
7
4
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
x
+
6
x
−
5
=
4
3
\frac{x+6}{x-5}=\frac{4}{3}
x
−
5
x
+
6
=
3
4
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
x
−
3
4
=
x
+
4
9
\frac{x-3}{4}=\frac{x+4}{9}
4
x
−
3
=
9
x
+
4
\newline
Answer:
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Solve for
x
\mathrm{x}
x
.
\newline
x
−
3
x
−
6
=
4
3
\frac{x-3}{x-6}=\frac{4}{3}
x
−
6
x
−
3
=
3
4
\newline
Answer:
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