Simplify \((216)^{-\frac{2}{3}} \times (0.16)^{-\frac{3}{2}}\)
FURTHER MATHEMATICS
WAEC 2009
Simplify \((216)^{-\frac{2}{3}} \times (0.16)^{-\frac{3}{2}}\)
- A. \(\frac{125}{288}\)
- B. \(\frac{2}{125}\)
- C. \(\frac{4}{225}\)
- D. \(\frac{2}{225}\)
Correct Answer: A. \(\frac{125}{288}\)
Explanation
\((216)^{-\frac{2}{3}} = (\frac{1}{216})^{\frac{2}{3}} = (\sqrt[3]{\frac{1}{216}})^{2} = (\frac{1}{6})^{2} = \frac{1}{36}\)
\((0.16)^{-\frac{3}{2}} = (\frac{100}{16})^{\frac{3}{2}} = (\sqrt{100}{16})^{3} = \frac{1000}{64}\)
\(\frac{1}{36} \times \frac{1000}{64} = \frac{125}{288}\)
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