# Calculating exterior powers

I am confused with an example I found, which says that for a given graded vector space $$V$$ such that $$V^0=0$$ and $$V^1=0$$, then $$(\bigwedge V)^2=\bigwedge^2V =V^2$$.

Two questions:

1.$$V^0$$ is not the ground field, right?But then what is it?

2.Why this is true and how is this justified?

Thanks!