How to work with exterior powers of exterior powers?

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I know Sage lets me work with exterior powers. I want to work with exterior powers of exterior powers: for example, for a vector space $V$, we can take $\bigwedge^2 \bigwedge^2 V$. In this space, $(a \wedge b) \wedge (a \wedge b) = 0$ but $(a \wedge b) \wedge (a \wedge c) \neq 0$.

Is there a way work in a space like this in Sage? If not, can someone help me get started?