If p^2 + q^2 - r^2 = 0, then the value of (p^6 + q^6 - r^6) ÷ p^2q^2r^2 is:

Let a = p², b = q², c = −r². Then a + b + c = 0, so a³ + b³ + c³ = 3abc, i.e. p⁶ + q⁶ − r⁶ = −3p²q²r². Dividing by p²q²r² gives −3.