Question

Simplify fourth root of 6 over fifth root of 6.

Answer 1

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

$\frac{1*5}{4*5} -\frac{1*4}{5*4}$

$\frac{5-4}{20} =\frac{1}{20}$

$6^{\frac{1}{4} -\frac{1}{5}}=6^\frac{1}{20}$

$6^\frac{1}{20} =\sqrt[20]{6}$

Answer 2

Simplified form would be twentieth root of 6