Simplify \(\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\)

  • A 25
  • B \(\frac{1}{5}\)
  • C 1
  • D \(\frac{1}{25}\)
waec 2006mathematics

The correct answer is C. 1

\(\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\) = \(\frac{25^{4 - \frac{1}{6}}}{(\frac{1}{5})^{-7 + \frac{1}{6}}}\)

= \(\frac{25^{\frac{1}{2}}}{(\frac{1}{5})^{-1}}\)

= \(\frac{(5^2)^{\frac{1}{2}}}{(5^{-1})^{-1}}\)

= \(\frac{5}{5}\)

= 1

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