$ \frac{a (a^2)^{\frac{1}{3}}}{(a\sqrt{a})^{\frac{1}{3}}} =\frac{a\times a^{\frac{2}{3}}}{a^{\frac{1}{3}}\times a^{\frac{1}{6}}}=\frac{a^{\frac{5}{3}}}{a^{\frac{3}{6}}}=\frac{a^{\frac{10}{6}}}{a^{\frac{3}{6}}}=a^{\frac{7}{6}}$