Solution
= Solution
Assume $M\times N$ is oriented. Fix $q\in N$ and an ordered basis $(w_1,\ldots,w_n)$ of $T_qN$. Contracting the product orientation successively with the constant vectors $w_i$ along $M\times\{q\}$ produces a nowhere-zero top form on $M$. Hence $M$ is orientable. Fixing a point and a basis in $M$ gives an orientation of $N$ in the same way. This is the <orientability of factors of a product manifold>.