$$\frac { ( - 2 x y ) ^ { 2 } } { 2 x ^ { - 3 } \cdot 2 x ^ { - 2 } y ^ { 2 } }$$
$x^{7}$
$$\frac{\left(-2xy\right)^{2}}{2x^{-5}\times 2y^{2}}$$
$$\frac{\left(-2\right)^{2}x^{2}y^{2}}{2x^{-5}\times 2y^{2}}$$
$$\frac{4x^{2}y^{2}}{2x^{-5}\times 2y^{2}}$$
$$\frac{4x^{2}y^{2}}{4x^{-5}y^{2}}$$
$$\frac{x^{2}}{x^{-5}}$$
$$x^{7}$$
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