Explanation:
\(\frac{19}{64}\)
\(\Big\{\Big(\frac{1}{3}\Big)^{-3}-\Big(\frac{1}{2}\Big)^{-3}\Big\}\div\Big(\frac{1}{4}\Big)^{-3}\)
\(=\Big\{\Big(\frac{3}{1}\Big)^{3}-\Big(\frac{2}{1}\Big)^{3}\Big\}\div\Big(\frac{4}{1}\Big)^{3}\) \(\text{As, }\text{x}^{-1}=\frac{1}{\text{x}}\)
\(=\{3^3-2^3\}\div4^3\)
\(=\{27-8\}\div64\)
\(=19\div64\)
\(=\frac{19}{64}\)
Hence, the correct alternative is option (a).