Answer
$- \frac{x^{11}}{3y^{36}}$.
Work Step by Step
The given expression is
$\Rightarrow \frac{-4x^8y^{-12}}{12x^{-3}y^{24}}$
Factor all the terms.
$\Rightarrow \frac{-2^2x^8y^{-12}}{2^2\cdot3x^{-3}y^{24}}$
Subtract the exponents when dividing.
$\Rightarrow -2^{(2-2)}\cdot 3^{-1}x^{(8+3)}y^{(-12-24)}$
Simplify.
$\Rightarrow -2^{0}\cdot 3^{-1}x^{11}y^{-36}$
$\Rightarrow - 3^{-1}x^{11}y^{-36}$
Rewrite in the fractions form
$\Rightarrow - \frac{x^{11}}{3y^{36}}$.
