# Simplify: -`root(3)(432)` ``

### 2 Answers | Add Yours

`-root(3)(432)`

write prime factors of 432

`432=2xx2xx2xx2xx3xx3xx3`

`` `432=2^4xx3^3` ,

we know

`(x xx y)^m=x^mxxy^m` ,therefore

`-root(3)(432)=-(432)^(1/3)`

`` `-(2^4xx3^3)^(1/3)=-(2^4)^(1/3)xx((3)^3)^(1/3)`

`=-(2)^(4/3)xx(3)^(3/3)`

`=-3xx2(2)^(1/3)`

`=-6root(3)(2)`

Ans.

`-root(3)(432)=-root(3)(2X216)=-root(3)(2X6^3)=-6root(3)(2)`