We have the expression
[tex]\frac{\sqrt[4]{6}}{\sqrt[5]{6}}[/tex]We can transform the radical into exponential, then
[tex]\frac{6^{\frac{1}{4}}}{6^{\frac{1}{5}}}[/tex]Now we can simplify the expression doing the division property
[tex]\frac{6^{\frac{1}{4}}}{6^{\frac{1}{5}}}=6^{\frac{1}{4}-\frac{1}{5}}[/tex]The new exponential will be
[tex]\frac{1}{4}-\frac{1}{5}=\frac{5-4}{20}=\frac{1}{20}[/tex]Therefore
[tex]6^{\frac{1}{4}-\frac{1}{5}}=6^{\frac{1}{20}}[/tex]The final answer is
