Question

Find the simplest RF of :
(a) `root(4)(216) and (b) root(5)(16)`

Answer 1

(a) `root(4)(216)=root(4)((2^(3))(3^(3)))=2^(3//4)xx3^(3//4)`
So RF is `2^(1//4)xx3^(1//4)=(2xx3)^(1//4)=root(4)(6)`
`therefore root(5)(16)=root(5)(2^(4))=2^(4//5)`
`therefore` RF is `2^(1//5) implies (2^(4//5))(2^(1//5))=2^(5//5)=1`
`therefore root(5)(2)` is the simplest RF of `root(5)(16)`