Question

What is the domain of this 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)=3w9. You need to find out the values of w for which f(w)=0. You have
f(w)=0⇔3w9=0⇔w9=0⇔w=9√0=0

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

Your domain is thus given by the set {x∈R∣x≠0}

The domain can also be written as (−∞,0)∪(0,+∞).