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2021 Fall AMC 12B Problems/Problem 4

Revision as of 01:05, 24 November 2021 by Nh14 (talk | contribs) (Created page with "== Problem == 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

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

The requested value is \[\frac{8^{2022}}{4} = \frac{2^{6066}}{4} = \frac{2^{6066}}{2^2} = 2^{6064} = 4^{3032}.\] Thus, the answer is $\boxed{(\textbf{E}) \: 4^{3032}}.$

~NH14

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