Evaluate (\(\frac{1}{343}\))\(^{\frac{1}{3}}\) + (64)\(^{-\frac{1}{3}}\) – \(\frac{4}{9}\)\(^{-\frac{1}{2}}\)
- -\(\frac{17}{36}\)
- -\(\frac{3}{28}\)
-
\(\frac{31}{28}\)
- \(\frac{17}{36}\)
- \(\frac{1}{4}\)
The correct answer is: C
Explanation
(\(\frac{1}{343}\))\(^{\frac{1}{3}}\) + (64)\(^{-\frac{1}{3}}\) - \(\frac{4}{9}\)\(^{-\frac{1}{2}}\)
where \(343 = 7^3, 64 = 2^6, 4 = 2^2, 9 = 3^2\)
\(7^{-3}\) \(^{\frac{1}{3}}\) + \(2^6\) \(^{\frac{-1}{3}}\) - \(\frac{2^2}{3^2}\) \(^{\frac{-1}{2}}\)
\(7^{-1} + 2^{-2} - (\frac{2}{3})^{-1}\)
\(\frac{1}{7} + \frac{1}{4} - \frac{3}{2}\)
\(\frac{4+7-42}{28}\)
\(\frac{31}{28}\)