Some concepts on 1-forms

Let $\omega_1$ and $\omega_2$ be 1-forms taken as

$\omega_1 = 3ydx + xdy \;\;\; \text{and} \;\;\; \omega_2 = -ydx + xdy.$

We say that a 1-form is exact when it can be expressed as $df$ for some function $f: U_f \subseteq \mathbb{R^2} \rightarrow \mathbb{R}$ . When a 1-form is not exact, one can make it exact by multiplying it by some function $\mu: U_\mu \subseteq \mathbb{R^2} \rightarrow \mathbb{R}$ called the integrating factor. If the integrating factors for $\omega_1$ and $\omega_2$ are $\mu_1(x, y) = x^{n_1}$ and $\mu_2(x, y) = x^{n_2},$ find

$n_1 \cdot n_2.$