Question

How do you simplify `³sqrt(24w^2)` divided by `³sqrt(3w^4)`?

Answer 1

Remember that if you have roots with the same exponent their arguments can be divided under a root with that exponent.
That is
`root(a)(b)/root(a)(c) = root(a)(b/c)`

For this particular example
`root(3)(24w^2)/root(3)(3w^4)`

`= root(3)((24w^2)/(3w^4))`

`= root(3)(8/w^2)`

`= 2 root(3)(1/w^2)`

`= 2/root(3)(w^2)`