2021 AMC 10B Fall Problem 5 — Solution | LIVE by Po-Shen Loh

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2021 AMC 10B Fall Problem 5

Attempt Problem 5 of the 2021 AMC 10B Fall below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10B Fall solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

Let $n=8^{2022}.$ Which of the following is equal to $\frac{n}{4}?$

$4^{1010}$

$2^{2022}$

$8^{2018}$

$4^{3031}$

$4^{3032}$

Answer: E

Concepts:exponent power of 2

Difficulty rating: 560

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 .

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