what is the domain of this function p (w) 2/3w^9

... ?

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) = 3 w9. You need to find out the values of w for which f (w) = 0. You have

f (w) = 0⇔3 w9 = 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,+∞).