sqrt(a^2sqrt(a^4,5),7)/sqrt(a,5)

$${\frac{{\sqrt[{{\mathtt{{\mathtt{7}}}}}]{{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{5}}}}}]{{{\mathtt{a}}}^{{\mathtt{4}}}}}}}}{{\sqrt[{{\mathtt{{\mathtt{5}}}}}]{{\mathtt{a}}}}}}$$

$$\\=\frac{\sqrt[7]{a^2\times a^{4*(1/5)}}}{a^{1/5}}\\\\ =\frac{\sqrt[7]{a^2\times a^{0.8}}}{a^{0.2}}\\\\ =\frac{\sqrt[7]{a^{2.8}}}{a^{0.2}}\\\\ =\frac{(a^{2.8})^{1/7}}{a^{0.2}}\\\\ =\frac{a^{2.8/7}}{a^{0.2}}\\\\ =\frac{a^{0.4}}{a^{0.2}}\\\\ =a^{0.4-0.2}\\\\ =a^{0.2}\\\\ =a^{1/5}\\\\ =\sqrt[5]{a}$$