((6x^6 y^-4)/(12x^-2 y^7))^-4

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If you have correctly written the problem as it appears here, the only thing you can do is to factor out a 2 from the bottom term: ((6x^6)(y^-4) / 2(6X6-y^7)).  Now divide by 2 and that is all you can do. (3X^6)(y^-4) / (6x6-y^7) You may have meant the bottom term to mean (12x^6 -2y^7) but that does not change your limited factoring opportunity.  You'll end up with 6X^6-y^7 as you denominator.  If this is what you meant, you can write  this as (3X^6) / (y^4)(6x^6-y^7) or finally you can say (3x^6) / ((6x^6)(y^4) - y^11).  This way all of the y term ends up on the bottom of the expression.