#### Answer

$= \frac{20a^{2}}{9bc^{2}}$

#### Work Step by Step

$\frac{10a^{3}}{6b^{2}c^{4}} \div \frac{15a}{20bc^{2}}$
$= \frac{10a^{3}}{6b^{2}c^{4}} \times \frac{20bc^{2}}{15a}$
$= \frac{200a^{3}bc^{2}}{90ab^{2}c^{4}}$
$= \frac{20a^{3}bc^{2}}{9ab^{2}c^{4}}$
$= \frac{abc^{2}(20a^{2})}{abc^{2}(9bc^{2})}$
$= \frac{20a^{2}}{9bc^{2}}$