Question

What is the domain of the function `p(w)=2/(3w^9)`?

Answer 1

You have a fractions, so the only thing you must be sure of is that the denominator is not zero.

In your case, the denominator is given by the function `f(w)=3w^9`. You need to find out the values of `w` for which `f(w)=0`. You have
`f(w)=0 \iff 3w^9=0 \iff w^9=0 \iff w=^9\sqrt0=0`

So, your only problem is `w=0`, and all other numbers are fine.

Your domain is thus given by the set `{x \in \mathbb{R} | x \ne 0}`

The domain can also be written as `(-oo,0)uu(0,+oo)`.