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2021 Fall AMC 10B Problems/Problem 5

Revision as of 21:54, 22 November 2021 by Kingofpineapplz (talk | contribs) (→‎Solution 1)

Problem 5

Let $n=8^{2022}$. Which of the following is equal to $\frac{n}{4}?$

$(\textbf{A})\: 4^{1010}\qquad(\textbf{B}) \: 2^{2022}\qquad(\textbf{C}) \: 8^{2018}\qquad(\textbf{D}) \: 4^{3031}\qquad(\textbf{E}) \: 4^{3032}$

Solution 1

We have \[n=8^{2022}= \left(8^\frac{2}{3}\right)^{2022}=4^{3033}.\] Therefore, \[\frac{n}4=\boxed{(\textbf{E})\:4^{3032}}.\]

~kingofpineapplz

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