Question

If $\frac{9^{{}^{\frac{1}{3}}}\times {27}^{-\frac{1}{2}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}$ is $m^{-\frac{1}{3}}$, then $m$ is equal to:

Answer 1

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

$=\frac{3^{\frac{2}{3}-\frac{3}{2}}}{3^{\frac{1-4}{6}}}$

$=\frac{3^{\frac{4-9}{6}}}{3^{-\frac{3}{6}}}$

$=\frac{3^{-\frac{5}{6}}}{3^{-\frac{3}{6}}}$

$=3^{(-\frac{5}{6}+\frac{3}{6})}$

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

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