[tex]\dfrac{(4x^4y^3)^3}{3(5x^2y^6)^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{4^3(x^4)^3(y^3)^3}{3(5^2)(x^2)^2(y^6)^2}=\dfrac{64x^{12}y^9}{3(25)x^4y^{12}}=\dfrac{64x^{12}y^9}{75x^4y^{12}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\dfrac{64}{75}x^{12-4}y^{9-12}=\dfrac{64}{75}x^8y^{-3}=\boxed{\dfrac{64x^8}{75y^3}}[/tex]
