2021 Fall AMC 10B Problem 5

Problem 5 of 25EasierAlgebra Number Theory

Let

n=8^{2022}.

Which of the following is equal to

\frac{n}{4}?

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Solution

Since

8=2^3,

we have

n=8^{2022}=2^{6066}=4^{3033}.

Therefore

\frac n4=\frac{4^{3033}}4=4^{3032}.

Thus, the answer is E .

Concepts: exponent · power of 2

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