Which of the following is equal to 2000 × 2000^2000?

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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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}

Concepts:exponent

Write the leading

2000

2000^1

Multiplying powers with the same base adds the exponents

Write the factor

2000

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.