Simplify \(\frac{25 ^\frac{2}{3} \div 25 ^\frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\)
- 25
- \(\frac{1}{5}\)
-
1
- \(\frac{1}{25}\)
The correct answer is: C
Explanation
\(\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\) = \(\frac{25^{4 - \frac{1}{6}}}{(\frac{1}{5})^{-7 + \frac{1}{6}}}\)
= \(\frac{25^{\frac{1}{2}}}{(\frac{1}{5})^{-1}}\)
= \(\frac{(5^2)^{\frac{1}{2}}}{(5^{-1})^{-1}}\)
= \(\frac{5}{5}\)
= 1