Question

Simplify fourth root of 6 over fifth root of 6.

Answer 1

Simplified form would be twentieth root of 6

Answer 2

`\sqrt[20]{6}`

Explanation:

we need to simplify

`\frac{\sqrt[4]{5}}{\sqrt[5]{6}}`

Each radical can be written in fraction form

`\sqrt[4]{6} = 6^{(1)/(4)}`

`\sqrt[5]{6} = 6^{(1)/(5)}`

`\frac{\sqrt[4]{5}}{\sqrt[5]{6}}=\frac{6^{(1)/(4)}}{6^{(1)/(5)}}`

Both top and bottom have same base so we subtract the exponents

`6^{(1)/(4) -(1)/(5)}`

Take common denominator to subtract the fractions

`(1*5)/(4*5) -(1*4)/(5*4)`

`(5-4)/(20) =(1)/(20)`

`6^{(1)/(4) -(1)/(5)}=6^(1)/(20)`

`6^(1)/(20) =\sqrt[20]{6}`