What is the value of the ratio 2^2001 × 3^20036^2002?

2002 AMC 10B Problem 1

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What is the value of the ratio

\dfrac{2^{2001} \cdot 3^{2003}}{6^{2002}}?

\dfrac{1}{6}

\dfrac{1}{3}

\dfrac{1}{2}

\dfrac{2}{3}

\dfrac{3}{2}

Concepts:exponent

Write

6^{2002}

2^{2002}\cdot 3^{2002}

Cancel the common powers of

2

and

3

from top and bottom

Since

6^{2002} = 2^{2002}\cdot 3^{2002},

the ratio becomes

\dfrac{2^{2001}\cdot 3^{2003}}{2^{2002}\cdot 3^{2002}} = \dfrac{3}{2}.

Thus, the correct answer is E.