\frac{a^{\frac{1}{5}\cdot 2}\cdot a^{-\frac{1}{10}}}{a^{-\frac{1}{2}}}=\frac{a^{\frac{2}{5}+(-\frac{1}{10})}}{a^{-\frac{1}{2}}}=\frac{a^{\frac{4}{10}+(-\frac{1}{10})}}{a^{-\frac{1}{2}}}=\frac{a^{\frac{3}{10}}}{a^{-\frac{1}{2}}}=[/m]
[m]=a^{\frac{3}{10}-(-\frac{1}{2})}=a^{\frac{3}{10}+\frac{5}{10}}=a^{\frac{8}{10}}[/m]