Exercise 7

Alice and Bob are considering posets $\bfP$ and $\bfQ$. They soon realize that $\bfQ$ is isomorphic to $\bfP^d$. After $10$ minutes of work, they figure out that $\bfP$ has height $5$ and width $3$. Bob doesn't want do find the height and width of $\bfQ$, since he figures it will take (at least) another $10$ minutes to answer these questions for $\bfQ$. Alice says Bob is crazy and that she already knows the height and width of $\bfQ$. Who's right and why?