2021 Fall AMC 10B Problems/Problem 5

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

2021 Fall AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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