2021 AMC 10 B Fall

Complete problem set with solutions and individual problem pages

Problem 5 Easy

Let n=8^{2022}. Which of the following is equal to \frac{n}{4} ?(2021 AMC Fall 10B, Question #5)

  • A.

    4^{1010}

  • B.

    2^{2022}

  • C.

    8^{2018}

  • D.

    4^{3031}

  • E.

    4^{3032}

Answer:E

Solution 1:

We have n=8^{2022}=\left(8^{\frac{2}{3}}\right)^{3033}=4^{3033} . Therefore, \frac{n}{4}=(\mathbf{E}) 4^{3032}

Solution 2:

The requested value is \frac{8^{2022}}{4}=\frac{2^{6066}}{4}=\frac{2^{6066}}{2^{2}}=2^{6064}=(\mathbf{E}) 4^{3032}

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