Correct Answer: Option C

Explanation

\(\frac{8^{\frac{2}{3}} \times 27^{\frac{-1}{3}}}{64^{\frac{1}{3}}}\)

Calculating each part:

1. \(8 = 2^3 \Rightarrow 8^{\frac{2}{3}} = 4\)

2. \(27 = 3^3 \Rightarrow 27^{\frac{-1}{3}} = \frac{1}{3}\)

3. \(64 = 4^3 \Rightarrow 64^{\frac{1}{3}} = 4\)

Now substituting these values:

\(\frac{4 \times \frac{1}{3}}{4} = \frac{1}{3}\)

Thus, the simplified expression is: \(\frac{1}{3}\)

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