Question

The seventh root of x divided by the eighth root of x is

Options

• x

• \[\sqrt{x}\]

• \[\sqrt[56]{x}\]

• \[\frac{1}{\sqrt[56]{x}}\]

Answer 1

We have to find he seventh root of x divided by the eighth root of x, so let it be L. So, 

`L= (7sqrtx)/(8sqrtx)`

`= (x^(1/7))/(x^(1/8))`

`= x^(1/7-1/8)`

`= x^((1xx8)/(7xx8)-(1 xx7) /(8 xx 7))`

`L = x^(8/56 -7/56)`

`=x^1/56`

`=56sqrtx`

The seventh root of x divided by the eighth root of x is `56sqrtx`

Hence the correct choice is c.