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
\(\frac{1}{4}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
(\(\frac{1}{343}\))\(^{\frac{1}{3}}\) + (64)\(^{-\frac{1}{3}}\) - \(\frac{4}{9}\)\(^{-\frac{1}{2}}\)
where \(343 = 7^3, 64 = 2^6, 4 = 2^2, 9 = 3^2\)
\(7^{-3}\) \(^{\frac{1}{3}}\) + \(2^6\) \(^{\frac{-1}{3}}\) - \(\frac{2^2}{3^2}\) \(^{\frac{-1}{2}}\)
\(7^{-1} + 2^{-2} - (\frac{2}{3})^{-1}\)
\(\frac{1}{7} + \frac{1}{4} - \frac{3}{2}\)
\(\frac{4+7-42}{28}\)
-\(\frac{31}{28}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #41952)