[tex]$\frac{\sqrt[3]{5}\sqrt{5}}{\sqrt[3]{5^5}}=\frac{5^{\frac{1}{3}}\cdot5^{\frac{1}{2}}}{5^{\frac{5}{3}}}=\frac{5^{\frac{1}{3}+\frac{1}{2}}}{5^{\frac{5}{3}}}=\frac{5^{\frac{5}{6}}}{5^{\frac{5}{3}}}=5^{\frac{5}{6}-\frac{5}{3}}=5^{-\frac{5}{6}}=\frac{1}{5^{\frac{5}{6}}}=\frac{1}{\sqrt[6]{5^5}}$[/tex]
