б) $$45a^{3}b \cdot \frac{c^{2}}{30a^{4}b}$$;

б) $$45a^{3}b \cdot \frac{c^{2}}{30a^{4}b} = \frac{45a^{3}bc^{2}}{30a^{4}b} = \frac{45}{30} \cdot \frac{a^{3}}{a^{4}} \cdot \frac{b}{b} \cdot c^{2} = \frac{3}{2} \cdot \frac{1}{a} \cdot 1 \cdot c^{2} = \frac{3c^{2}}{2a}$$.

Ответ: $$\frac{3c^{2}}{2a}$$