2000 AMC 12 Problem 2

Attempt Problem 2 of the 2000 AMC 12 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 12 solutions, or check the answer key.

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

What is

2000(2000^{2000})?

2000^{2001}

4000^{2000}

2000^{4000}

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

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

Concepts:exponent

Write the leading factor as

2000^1

Multiplying powers of the same base adds the exponents

Writing

2000 = 2000^1,

we get

\begin{gathered} 2000^1 \cdot 2000^{2000} \\ = 2000^{1 + 2000} \\ = 2000^{2001}. \end{gathered}

All of the other options are larger than this.

Thus, the correct answer is A.

Problem 2 in other years