Let M and N be orientable m- and n-manifolds, respectively. Prove that their product is an orientable (m+n)-manifold.
An m-manifold M is orientable iff it has a nowhere vanishing m-form.
The Attempt at a Solution
I assume I would take nowhere vanishing m- and n-forms f and g on M and N, respectively, and use them to construct an (m+n)-form h on MxN. However I don't know how this construction would proceed. Any help would be much appreciated.