9.
[tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}[/tex]
Using the following properties:
[tex]\begin{gathered} x^a\cdot x^b=x^{a+b} \\ a^{-x}=\frac{1}{a^x} \\ \sqrt[z]{x^y}=x^{\frac{y}{z}} \end{gathered}[/tex][tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}=5^{\frac{7}{2}}\cdot5^{\frac{6}{2}}\cdot5^{-\frac{3}{5}}=5^{\frac{7}{2}+\frac{6}{2}-\frac{3}{5}}=5^{\frac{59}{10}}[/tex]
