Simplify \(\left(\frac{16}{81}\right)^{-\frac{3}{4}}\times \sqrt{\frac{100}{81}}\)

A.

\(\frac{80}{243}\)

B.

\(\frac{1}{64}\)

C.

\(\frac{25}{6}\)

D.

\(\frac{15}{4}\)

Correct answer is D

\(\left(\frac{16}{81}\right)^{-\frac{3}{4}}\times \sqrt{\frac{100}{81}}\\
\frac{1}{\left(\sqrt[4]{\frac{16}{81}}\right)^3}\times \frac{10}{9}=\frac{1}{\left(\frac{2}{3}\right)^3}\times\frac{10}{9}\\
=\frac{27}{8}\times \frac{10}{9}=\frac{15}{4}\)