simplify

$$\\\frac{2X^{-3}Y^2*(2Y)^{-2}}{2X^{-4}Y^2}\\\\
=\frac{\not{2}X^{(-3--4)}Y^2*2^{-2}Y^{(-2-2)}}{\not{2}}\\\\
=\frac{X^{1}Y^2*2^{-2}Y^{-4}}{1}\\\\
=\frac{X^{1}*2^{-2}Y^{(2-4)}}{1}\\\\
=\frac{X*2^{(-2)}Y^{(-2)}}{1}\\\\
=\frac{X}{1*2^{(+2)}Y^{(+2)}}\\\\
=\frac{X}{4Y^{2}}\\\\$$