Chapter 4 - Polynomials - 4.2 Negative Exponents and Scientific Notations - 4.2 Exercise Set - Page 244: 86

$-\dfrac{4y^{11}}{x^{3}}$

Using the laws of exponents, the given expression, $ \dfrac{12x^{-2}y^4}{-3xy^{-7}} $, is equivalent to \begin{array}{l}\require{cancel} \dfrac{\cancel{-3}\cdot(-4)x^{-2-1}y^{4-(-7)}}{\cancel{-3}xy^{-7}} \\\\= -4x^{-3}y^{11} \\\\= -\dfrac{4y^{11}}{x^{3}} .\end{array}