2000 AMC 10 Problem 2 — Solution | LIVE by Po-Shen Loh

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2000 AMC 10 Problem 2

Attempt Problem 2 of the 2000 AMC 10 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 2000 AMC 10 solutions, or check the answer key.

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2.

Which of the following is equal to $2000 \cdot 2000^{2000}?$

$2000^{2001}$

$4000^{2000}$

$2000^{4000}$

$4{,}000{,}000^{2000}$

$2000^{4{,}000{,}000}$

Answer: A

Concepts:exponent

Difficulty rating: 870

Solution:

Write the factor $2000$ as $2000^1.$ Then $\begin{aligned} 2000^1 \cdot 2000^{2000} &= 2000^{1 + 2000} \\ &= 2000^{2001}. \end{aligned}$

Each of the other options is larger than $2000^{2001}.$

Thus, the correct answer is A.

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