[tex]\left(\dfrac{(x^{-3})(y^2)}{(x^4)(y^6)}\right)^3\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\(x^{-3-4}y^{2-6})^3=(x^{-7}y^{-4})^3\\\\\text{use}\ (a\cdot b)^n=a^n\cdot b^n\\\\=(x^{-7})^3(y^{-4})^3\\\\\text{Use}\ (a^n)^m=a^{nm}\\\\=x^{(-7)(3)}y^{(-4)(3)}=\boxed{x^{-21}y^{-12}}[/tex]
