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Math Problems
Grade 8
Negative Exponents
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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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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(
4
−
2
×
4
−
3
)
3
(4^{-2} \times 4^{-3})^{3}
(
4
−
2
×
4
−
3
)
3
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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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1
1
1
. Add
4
x
3
−
2
x
2
+
1
4 x^{3}-2 x^{2}+1
4
x
3
−
2
x
2
+
1
to
7
x
2
+
12
x
7 x^{2}+12 x
7
x
2
+
12
x
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(
z
4
/
6
2
)
−
3
(z^4/6^2)^{-3}
(
z
4
/
6
2
)
−
3
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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
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Algebra Review
\newline
Question
2
2
2
of
35
35
35
(
1
1
1
point) | Question Attempt:
1
1
1
of
1
1
1
\newline
=
1
=
3
=
4
=1\quad=3\quad=4
=
1
=
3
=
4
\newline
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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Solve for
x
\mathrm{x}
x
.
\newline
4
x
+
2
3
=
x
+
3
2
\frac{4 x+2}{3}=\frac{x+3}{2}
3
4
x
+
2
=
2
x
+
3
\newline
Answer:
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P
(
t
)
=
30
(
2
)
(
t
18
)
P(t)=30(2)^{\left(\frac{t}{18}\right)}
P
(
t
)
=
30
(
2
)
(
18
t
)
\newline
The function models
P
P
P
, the amount of bacteria, in colony-forming units, in a bacteria culture after
t
t
t
minutes of growth. How many colony-forming units of bacteria are in the bacteria culture after
90
90
90
minutes?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
×
1
0
2
3\times10^{2}
3
×
1
0
2
\newline
(B)
9.6
×
1
0
2
9.6 \times10^{2}
9.6
×
1
0
2
\newline
(C)
5.4
×
1
0
3
5.4 \times10^{3}
5.4
×
1
0
3
\newline
(D)
2.43
×
1
0
7
2.43 \times10^{7}
2.43
×
1
0
7
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
4
÷
1
2
\frac{1}{4} \div \frac{1}{2}
4
1
÷
2
1
\newline
Answer:
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Use the distributive property to write an equivalent expression.
\newline
3
(
9
q
+
4
r
−
1
)
3(9 q+4 r-1)
3
(
9
q
+
4
r
−
1
)
\newline
Answer:
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Use the distributive property to write an equivalent expression.
\newline
3
(
5
v
−
8
w
+
10
)
3(5 v-8 w+10)
3
(
5
v
−
8
w
+
10
)
\newline
Answer:
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Convert the decimal below to a fraction in simplest form.
\newline
0.365
0.365
0.365
\newline
Answer:
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Convert the decimal below to a fraction in simplest form.
\newline
0.515
0.515
0.515
\newline
Answer:
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Suppose the diameter of a circle is
6
6
6
units. What is its circumference?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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Suppose the radius of a circle is
8
8
8
units. What is its circumference?
\newline
Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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Find the area of a circle with a circumference of
50
50
50
.
24
24
24
units.
\newline
□
\square
□
units
2
^{2}
2
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Rewrite the fraction as a decimal.
\newline
13
10
=
\frac{13}{10}=
10
13
=
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Rewrite the fraction as a decimal.
\newline
82
5
=
\frac{82}{5}=
5
82
=
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Rewrite the fraction as a decimal.
\newline
57
5
=
\frac{57}{5}=
5
57
=
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Rewrite the fraction as a decimal.
\newline
69
4
=
\frac{69}{4}=
4
69
=
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Rewrite the fraction as a decimal.
\newline
7
4
=
\frac{7}{4}=
4
7
=
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Rewrite the fraction as a decimal.
\newline
19
50
=
\frac{19}{50}=
50
19
=
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Rewrite the fraction as a decimal.
\newline
33
25
=
\frac{33}{25}=
25
33
=
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Rewrite the fraction as a decimal.
\newline
15
4
=
\frac{15}{4}=
4
15
=
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Rewrite the fraction as a decimal.
\newline
94
5
=
\frac{94}{5}=
5
94
=
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lim
x
→
−
3
x
3
+
x
2
−
6
x
x
2
+
3
x
=
\lim _{x \rightarrow-3} \frac{x^{3}+x^{2}-6 x}{x^{2}+3 x}=
lim
x
→
−
3
x
2
+
3
x
x
3
+
x
2
−
6
x
=
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lim
x
→
−
5
10
x
2
+
50
x
x
2
−
25
=
\lim _{x \rightarrow-5} \frac{10 x^{2}+50 x}{x^{2}-25}=
lim
x
→
−
5
x
2
−
25
10
x
2
+
50
x
=
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lim
x
→
−
1
x
4
+
2
x
3
+
x
2
x
+
1
=
\lim _{x \rightarrow-1} \frac{x^{4}+2 x^{3}+x^{2}}{x+1}=
lim
x
→
−
1
x
+
1
x
4
+
2
x
3
+
x
2
=
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lim
x
→
4
−
5
x
2
+
20
x
x
3
−
3
x
2
−
4
x
=
\lim _{x \rightarrow 4} \frac{-5 x^{2}+20 x}{x^{3}-3 x^{2}-4 x}=
lim
x
→
4
x
3
−
3
x
2
−
4
x
−
5
x
2
+
20
x
=
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lim
x
→
2
x
4
+
3
x
3
−
10
x
2
x
2
−
2
x
=
\lim _{x \rightarrow 2} \frac{x^{4}+3 x^{3}-10 x^{2}}{x^{2}-2 x}=
lim
x
→
2
x
2
−
2
x
x
4
+
3
x
3
−
10
x
2
=
Get tutor help
Apply the distributive property to create an equivalent expression.
\newline
5
×
(
−
2
w
−
4
)
=
5 \times(-2 w-4)=
5
×
(
−
2
w
−
4
)
=
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Apply the distributive property to create an equivalent expression.
\newline
(
3
−
8
y
)
⋅
(
−
2.5
)
=
(3-8 y) \cdot(-2.5)=
(
3
−
8
y
)
⋅
(
−
2.5
)
=
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