[tex]\frac{24b^{2}c^{3} }{3a^{6} } : \frac{16bc}{a^{5} } } = \frac{24b^{2}c^{3} }{3a^{6} } * \frac{a^{5}}{16bc} = \frac{3bc^{2} }{3a} * \frac{1}{2} = \frac{bc^{2} }{2a}[/tex]
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[tex]\frac{24b^{2}c^{3} }{3a^{6} } : \frac{16bc}{a^{5} } } = \frac{24b^{2}c^{3} }{3a^{6} } * \frac{a^{5}}{16bc} = \frac{3bc^{2} }{3a} * \frac{1}{2} = \frac{bc^{2} }{2a}[/tex]