  The Arens products are the standard way of extending the product from a
Banach algebra $\mc A$ to its bidual $\mc A''$. Ultrapowers provide another
method which is more symmetric, but one that in general will only give a
bilinear map, which may not be associative. We show that if $\mc A$ is Arens
regular, then there is at least one way to use an ultrapower to recover the
Arens product, a result previously known for C$^*$-algebras. Our main tool is a
Principle of Local Reflexivity result for modules and algebras.
