If p + q + r = 0, then what is (p²/z^(qr)) × (q²/z^(rp)) × (r²/z^(pq)) equal to?

The expression simplifies to z^((p² + q² + r²)/(pqr)) — wait, more carefully: the product is z^(p²/qr) × z^(q²/rp) × z^(r²/pq) = z^((p³ + q³ + r³)/(pqr)). When p + q + r = 0, we have the identity p³ + q³ + r³ = 3pqr. So the exponent becomes 3pqr/pqr = 3, giving z³. Hmm, but checking the standard identity: if p+q+r=0 then p³+q³+r³ = 3pqr. So the answer is z³.