Simplify each of the following: (i) `root(5)(16)xxroot(5)(2)` (ii) `root(4)(243)/root(4)(3)`

Explanation

(i) Given :
`root(5)(16)xxroot(5)(2)`
`=(2^4)^(1/5)xx2^(1/5)`
`=2^(4/5+1/5)`
`=2^((4+1)/5)=2^1=2`
(ii) Given :
`root(4)(243)/root(4)(3)`
`=root(4)(3^5)/root(4)(3)`
`=3^(5xx1/4)/3^(1/4)`
`=3^(5/4-1/4)=3^((5-1)/4)=3^1=3`