Simplify (frac{9^{frac{1}{3}} times 27^{-frac{1}{3}}}{3^{-frac{1}{6}} times 3^{frac{2}{3}}})
-
A.
(frac{1}{3}) -
B.
1 -
C.
3 -
D.
9
Correct Answer: Option B
Explanation
(frac{9^{frac{1}{3}} times 27^{-frac{1}{3}}}{3^{-frac{1}{6}} times 3^{frac{2}{3}}}) = (frac{(3^2)^{frac{1}{3}} times (3^3)^{-frac{1}{3}}}{3^{-frac{1}{6}} times 3^{frac{2}{3}}})
= (frac{3^{frac{2}{3}} times 3^{frac{2}{3}}}{3^{-frac{1}{6}} times 3^{frac{2}{3}}})
= (frac{3^{frac{5}{6}}}{3^{-frac{5}{6}}})
= 1