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Math Problems
Grade 8
Multiply powers: integer bases
Determine if the following statements are logically equivalent.
\newline
(
p
∧
∼
q
)
→
r
≡
∼
(
p
∧
∼
q
)
∨
r
(p \wedge \sim q) \rightarrow r \equiv \sim(p \wedge \sim q) \vee r
(
p
∧
∼
q
)
→
r
≡∼
(
p
∧
∼
q
)
∨
r
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Simplify.
\newline
−
(
x
+
5
)
+
2
x
-(x+5)+2 x
−
(
x
+
5
)
+
2
x
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Evaluate the expression.
\newline
5
0
⋅
5
3
5^{0} \cdot 5^{3}
5
0
⋅
5
3
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\(4^
5
5
5
)(
4
4
4
^
2
2
2
)^
3
3
3
\
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f
(
x
)
=
5
⋅
2
x
f(x)=5 \cdot 2^{x}
f
(
x
)
=
5
⋅
2
x
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x
3
−
81
x
x^{3}-81 x
x
3
−
81
x
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(
n
+
k
−
1
n
−
1
)
\left(\begin{array}{c}n+k-1 \\ n-1\end{array}\right)
(
n
+
k
−
1
n
−
1
)
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6
5
3
+
2
40
3
6 \sqrt[3]{5}+2 \sqrt[3]{40}
6
3
5
+
2
3
40
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\(4^
6
6
6
)(
4
4
4
^{
−
8
-8
−
8
})\
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(
4
∧
−
3
∗
2
∧
−
3
)
∧
0
\left(4^{\wedge}-3 * 2^{\wedge}-3\right)^{\wedge} 0
(
4
∧
−
3
∗
2
∧
−
3
)
∧
0
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(
4
−
3
∗
2
−
3
)
0
(4^{-3}*2^{-3})^{0}
(
4
−
3
∗
2
−
3
)
0
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Differentiate
f
(
x
)
=
tan
(
3
x
2
+
2
x
)
f(x)=\tan(3x^{2}+2x)
f
(
x
)
=
tan
(
3
x
2
+
2
x
)
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