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AMC 10
2021 AMC 10 Fall
5
11167441797941771759046420316390396514938496893322604983025181998369218899143084
11167441797941771759046420316390396514938496893322604983025181998369218899143084
Source: 2021 Fall AMC10B P5
November 17, 2021
AMC
AMC 10
AMC 10 B
AMC 12
AMC 12 B
Problem Statement
Let
n
=
8
2022
n = 8^{2022}
n
=
8
2022
. Which of the following is equal to
n
4
\frac{n}{4}
4
n
?
<
s
p
a
n
c
l
a
s
s
=
′
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a
t
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x
−
b
o
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d
′
>
(
A
)
<
/
s
p
a
n
>
4
1010
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
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>
(
B
)
<
/
s
p
a
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>
2
2022
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
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x
−
b
o
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′
>
(
C
)
<
/
s
p
a
n
>
8
2018
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
4
3031
<
s
p
a
n
c
l
a
s
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=
′
l
a
t
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x
−
b
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>
(
E
)
<
/
s
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a
n
>
4
3032
<span class='latex-bold'>(A) </span>4^{1010}\qquad<span class='latex-bold'>(B) </span>2^{2022}\qquad<span class='latex-bold'>(C) </span>8^{2018}\qquad<span class='latex-bold'>(D) </span>4^{3031}\qquad<span class='latex-bold'>(E) </span>4^{3032}
<
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p
an
c
l
a
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=
′
l
a
t
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x
−
b
o
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d
′
>
(
A
)
<
/
s
p
an
>
4
1010
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
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d
′
>
(
B
)
<
/
s
p
an
>
2
2022
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
8
2018
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
4
3031
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
4
3032
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