Simplify \(\left(\frac{16}{81}\right)^{-\frac{3}{4}}\times \sqrt{\frac{100}{81}}\)
MATHEMATICS
WAEC 2000
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: D. \(\frac{15}{4}\)
Explanation
\(\left(\frac{16}{81}\right)^{-\frac{3}{4}}\times \sqrt{\frac{100}{81}}\\
\frac{1}{\left(\sqrt[4]{\frac{16}{81}}\right)^3}\times \frac{10}{9}=\frac{1}{\left(\frac{2}{3}\right)^3}\times\frac{10}{9}\\
=\frac{27}{8}\times \frac{10}{9}=\frac{15}{4}\)
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