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 \(\frac{15}{4}\)
waec 2000mathematics

The correct answer is D. \(\frac{15}{4}\)

\(\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}\)

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