1. **State the problem:** Simplify the expression $$\frac{5c^3d^2}{1.5c^4d^{14}}$$. 2. **Write the formula and rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{5}{1.5} = \frac{5}{\cancel{1.5}} \times \frac{\cancel{1}}{1} = \frac{5}{1.5} = \frac{10}{3}$$. 4. **Simplify the variables:** - For $c$: $$\frac{c^3}{c^4} = c^{3-4} = c^{-1} = \frac{1}{c}$$. - For $d$: $$\frac{d^2}{d^{14}} = d^{2-14} = d^{-12} = \frac{1}{d^{12}}$$. 5. **Combine all parts:** $$\frac{5c^3d^2}{1.5c^4d^{14}} = \frac{10}{3} \times \frac{1}{c} \times \frac{1}{d^{12}} = \frac{10}{3cd^{12}}$$. **Final answer:** $$\frac{10}{3cd^{12}}$$