  Exterior power operations on the higher $K$-groups of a quasi-compact scheme
have recently been constructed by Taelman and the authors by purely algebraic
means. In this paper, we prove two formulae that help to compute these
operations. The first is a formula for exterior powers of external products.
The second is a formula for exterior powers of $n$-cubes, i.e., of acyclic
binary multi-complexes supported on $[0,1]^n$. These formulae provide evidence
for the expectation that our exterior power operations agree with those defined
by Hiller.
