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2021 Fall AMC 10B Problems/Problem 5

Revision as of 20:52, 22 November 2021 by Kingofpineapplz (talk | contribs) (Created page with "==Problem 5== Let <math>n=8^{2022}</math>. Which of the following is equal to <math>\frac{n}{4}?</math> <math>(\textbf{A})\: 4^{1010}\qquad(\textbf{B}) \: 2^{2022}\qquad(\tex...")
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Problem 5

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

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

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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