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: 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
