# Exterior algebra of a direct sum

Can someone provide a formula for $$\bigwedge( V_1\oplus V_2\oplus V_3\oplus..)$$. The formula for two summands is $$\bigwedge^1 (V_1\oplus V_2)=(\wedge^1V_1\otimes \wedge^0V_2) \oplus (\wedge^0V_1\otimes\wedge^1V_2)$$ where $$V_1,V_2$$ are $$K$$-vector spaces.

Also am I right to assume that $$V_1\otimes K=V_1$$?