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})
Correct Answer: Option 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