$$\frac{3}{2}a^{2}b^{6}\div\frac{3}{8}a^{6}b^{2}=$$
$4\left(ab\right)^{8}$
$$\frac{\frac{3}{2}a^{2}b^{6}\times 8}{3}a^{6}b^{2}$$
$$\frac{12a^{2}b^{6}}{3}a^{6}b^{2}$$
$$4a^{2}b^{6}a^{6}b^{2}$$
$$4a^{8}b^{6}b^{2}$$
$$4a^{8}b^{8}$$
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$32a^{7}b^{8}$
