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