Why does every 7-manifold bound an 8-manifold? I'm glancing over Milnor's paper on exotic 7-spheres, and one of the first few lines says, `every closed 7-manifold $M^7$ is the boundary of an 8-manifold $B^8$. 
Here's what I don't understand: The unoriented cobordism ring is isomorphic to a polynomial ring over $\mathbb{Z}_2$ with a generator in every degree except $2^m -1$ for any $m$. In particular, there are generators $x_2$ and $x_5$ in degrees $2$ and $5$, respectively. So: why does their product not represent a nontrivial element of the group of cobordism classes of 7-manifolds?
Apologies if this is a silly question... I'm new to all of this. 

Because all its Stiefel-Whitney numbers are all zero.
