$$(3x^{-2}y^{-3})^{-4}$$
$\frac{x^{8}y^{12}}{81}$
$$\left(3x^{-2}y^{-3}\right)^{-4}$$
$$3^{-4}\left(x^{-2}\right)^{-4}\left(y^{-3}\right)^{-4}$$
$$\frac{1}{81}\left(x^{-2}\right)^{-4}\left(y^{-3}\right)^{-4}$$
$$\frac{1}{81}x^{-2\left(-4\right)}y^{-3\left(-4\right)}$$
$$\frac{1}{81}x^{8}y^{-3\left(-4\right)}$$
$$\frac{1}{81}x^{8}y^{12}$$
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