The simplified form of \frac{(6^{-1} \times \sqrt{216})^4}{1296} is:

  1. A. \frac{1}{36} ✓
  2. B. \frac{1}{1296}
  3. C. \frac{1}{6}
  4. D. \frac{1}{216}

Correct Answer: A. \frac{1}{36}

Explanation

\sqrt{216} = 6^{3/2}. The numerator is (6^{-1} \times 6^{3/2})^4 = (6^{1/2})^4 = 6^2 = 36. The denominator is 1296 = 6^4. Thus, \frac{36}{1296} = \frac{1}{36}.

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