If $\bigwedge^n V=0$, what can we say about the dimension of the vector space $V$ over an algebraically closed field $\mathbb{k}$?

Question

The question is this: if the wedge product $\bigwedge^n V=0$, what can we say about the dimension of the vector space $V$? Because $\bigwedge^n V=0$ for all $n>d$, where $\dim V=d<\infty$; but in the first case I don't know what to say. Thanks for your help!