Question

Solve

$\frac{3\times 9^{\frac{1}{3}}\times {27}^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}$

Answer 1

$\frac{3\times 9^{\frac{1}{3}}\times {27}^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}$

$=\frac{3\times 3^{\frac{2}{3}}\times 3^{-\frac{3}{2}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}$

$=\frac{3^{1+\frac{2}{3}-\frac{3}{2}}}{3^{\frac{1}{6}-\frac{2}{3}}}$

$=\frac{3^{-\frac{1}{2}}}{3^{-\frac{1}{2}}}$

$=1$