$$\frac{32x^{16}y^{3}}{8x^{5}y^{4}}=$$
$\frac{4x^{11}}{y}$
$$\frac{32^{1}x^{16}y^{3}}{8^{1}x^{5}y^{4}}$$
$$\frac{32^{1}}{8^{1}}x^{16-5}y^{3-4}$$
$$\frac{32^{1}}{8^{1}}x^{11}y^{3-4}$$
$$\frac{32^{1}}{8^{1}}x^{11}\times \frac{1}{y}$$
$$4x^{11}\times \frac{1}{y}$$
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$\frac{44x^{10}}{y}$
$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32y^{3}}{8y^{4}}x^{16-5})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{y}x^{11})$$
$$11\times \frac{4}{y}x^{11-1}$$
$$\frac{44}{y}x^{10}$$
