#### Answer

$\dfrac{9y^6}{x^8}$

#### Work Step by Step

RECALL:
(i) $(a^m)^n = a^{mn}$
(ii) $(ab)^m = a^mb^m$
(iii) $a^{-m} = \dfrac{1}{a^m}, a \ne0$
Use the rules above to have
$3^2(x^{-4})^2(y^3)^2
\\=9x^{-4(2)}y^{3(2)}
\\=9x^{-8}y^6
\\=\dfrac{9y^6}{x^8}.$