$$\frac{ 4 { x }^{ 2 } }{ 5y } \div \frac{ 2 { x }^{ 4 } }{ 10 { y }^{ 3 } } \times \frac{ { x }^{ 3 } }{ 2y }$$
$2xy$
$$\frac{4x^{2}\times 10y^{3}}{5y\times 2x^{4}}\times \frac{x^{3}}{2y}$$
$$\frac{2\times 2y^{2}}{x^{2}}\times \frac{x^{3}}{2y}$$
$$\frac{4y^{2}}{x^{2}}\times \frac{x^{3}}{2y}$$
$$\frac{4y^{2}x^{3}}{x^{2}\times 2y}$$
$$2xy$$
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$2y$