Question

How do you write `(6x^(1/2))/(15x^(2/3))` in radical form?

Answer 1

`6/(15root(6)x)`.

Explanation:

By application of the laws of exponents and surds which state that `x^(m/n)=root(n)(x^m)`, as well as the laws of exponents stating `(x^m)/(x^n)=x^(m-n) and x^(-n)=1/(x^n)`,
we may write this expression as

`6/15x^(1/2-2/3)=6/15x^(-1/6)=6/(15x^(1/6))=6/(15root(6)x)`.