Question

How do I simplify the 6th root of 4 divided by the 3rd root of 4?

Answer 1

so remember some exponentional laws


`x^(m/n) = \sqrt[n]{x^m}`


`(x^n)/(x^m)=x^(n-m)` and


`x^(-n)= (1)/(x^(n))`
so

4 to the 6th root=4^(1/6)
4 to the 3rd root=4^(1/3)

so

`(4^(1/6))/(4^(1/3)) =4^((1/6)-(1/3))=4^((1/6)-(2/6))=4^(-1/3)`
and
`4^(-1/3)= (1)/(4^(1/3))= \frac{1}{ \sqrt[3]{4} }`

the answer is
`\frac{1}{ \sqrt[3]{4} }`