Explanation

By the laws of exponents, z^{p²/qr} · z^{q²/rp} · z^{r²/pq} = z^{p²/qr + q²/rp + r²/pq}, and the exponent over the common denominator pqr is (p³+q³+r³)/pqr. The identity p+q+r=0 implies p³+q³+r³=3pqr, so the exponent collapses to 3pqr/pqr=3. Hence the product equals z³, option D. A common error is trying to evaluate each factor separately instead of adding the exponents first.