Evaluating Symmetrical Expressions

Algebra Level 4

(x3y3)2(xy)3+(y3z3)2(yz)3+(z3x3)2(zx)3 \dfrac{ ( x^3 - y^3) ^2 } { (xy)^3 } + \dfrac{ ( y^3 - z^3 )^2 } { (yz)^3} + \dfrac{ ( z^3 - x^3 ) ^2 } { ( zx)^3 } If x3+y3+z3=0 x^3 + y^3 + z^3 = 0 and xyz0 xyz \neq 0 , what is the value of the expression above.

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