If x and y are positive integers, which of the following is NOT a possible value for $\frac{32^x18^x}{6^{(x+y)}}$ ?

Correct answer marked below

\frac{1}{12}

\frac{1}{2}

\frac{2}{3}

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Explanation

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Official Explanation

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\frac{3*2^x*18^x}{6^{(x+y)}}=\frac{3*(2*18)^x}{6^x*6^y}=\frac{3*6^{2x}}{6^x*6^y}=\frac{3*6^x}{6^y}=3*6^{(x-y)}

As x and y are integers, (x-y) can be:

- For (x-y) = -2 → the expression becomes

\frac{3}{36}=\frac{1}{12}

- For (x-y) = -1 → the expression becomes

\frac{3}{6}=\frac{1}{2}

…

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What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.