A smooth $n$-manifold $N$ is called parallelizable if it admits $n$ smooth vector fields $Y_1;\ :\ :\ :\ ;\ Y_n$ that are linearly independent at every point $p$ in $M$.
How would I show if if $N_1, \ldots, N_k$ are parallelizable manifolds, then so is $N_1\times\cdots\times N_k$?