2021 Fall AMC 12B Problem 4

Problem 4 of 25EasierAlgebra

Let

n = 8^{2022}.

Which of the following is equal to

\dfrac{n}{4}?

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Solution

Write

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

Then

\dfrac{n}{4} = \dfrac{2^{6066}}{2^{2}} = 2^{6064}.

Since

2^{6064} = 4^{3032},

this matches the last option. Thus, the correct answer is E.

Concepts: exponent

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.