Evaluate (\(\frac{1}{343}\))\(^{\frac{1}{3}}\) + (64)\(^{-\frac{1}{3}}\) - \(\frac{4}{9}\)\(^{-\frac{1}{2}}\)

A.

-\(\frac{17}{36}\)

B.

-\(\frac{3}{28}\)

C.

\(\frac{31}{28}\)

D.

\(\frac{17}{36}\)

E.

\(\frac{1}{4}\)

Correct answer is C

(\(\frac{1}{343}\))\(^{\frac{1}{3}}\) + (64)\(^{-\frac{1}{3}}\) - \(\frac{4}{9}\)\(^{-\frac{1}{2}}\)

where \(343 = 7^3,  64 = 2^6,  4 = 2^2,  9 = 3^2\)

\(7^{-3}\) \(^{\frac{1}{3}}\) + \(2^6\) \(^{\frac{-1}{3}}\) - \(\frac{2^2}{3^2}\) \(^{\frac{-1}{2}}\) 

\(7^{-1} + 2^{-2} - (\frac{2}{3})^{-1}\)

\(\frac{1}{7} + \frac{1}{4} - \frac{3}{2}\)

\(\frac{4+7-42}{28}\)

\(\frac{31}{28}\)