Question

How do you simplify expressions involving variables such as `(27p^3q^12)^(1/3)`?

Answer 1

`a^(1/3)` is the third root of `x` or `root(3)(x)`
so what we want to try to do is express the components of `x` as powers of `3` (as much as possible).

Note also that

`root(n)(s*t) = root(n)(s) * root(n)(t)`

For the given example
`(27p^3q^(12))^(1/3)`

`= (3^3* p^3* (q^4)^3)^(1/3)`

`= root(3)(3^3) * root(3)(p^3) *root(3)((q^4)^3)`

`=3pq^4`