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Evaluate \(\cfrac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\)


Question

Evaluate \(\cfrac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\)

Options

A) \(\frac{23}{5}\)

B) -\(\frac{23}{5}\)

C) \(\frac{1}{8}\)

D) \(\frac{21}{7}\)

The correct answer is C.

Explanation:

\(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\)
\(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\) = \(\frac{3\sqrt{27} - 3\sqrt{8}^2}{\sqrt{16} \times 2}\)
\(\frac{3 - 4}{4 \times 2}\)
= \(\frac{-1}{8}\)

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