Answer:
[tex]\sqrt[20]{6}[/tex]
Step-by-step explanation:
we need to simplify
[tex]\frac{\sqrt[4]{5}}{\sqrt[5]{6}}[/tex]
Each radical can be written in fraction form
[tex]\sqrt[4]{6} = 6^{\frac{1}{4}}[/tex]
[tex]\sqrt[5]{6} = 6^{\frac{1}{5}}[/tex]
[tex]\frac{\sqrt[4]{5}}{\sqrt[5]{6}}=\frac{6^{\frac{1}{4}}}{6^{\frac{1}{5}}}[/tex]
Both top and bottom have same base so we subtract the exponents
[tex]6^{\frac{1}{4} -\frac{1}{5}}[/tex]
Take common denominator to subtract the fractions
[tex]\frac{1*5}{4*5} -\frac{1*4}{5*4}[/tex]
[tex]\frac{5-4}{20} =\frac{1}{20}[/tex]
[tex]6^{\frac{1}{4} -\frac{1}{5}}=6^\frac{1}{20}[/tex]
[tex]6^\frac{1}{20} =\sqrt[20]{6}[/tex]
