1. **State the problem:** Simplify the expression $$(10c^6 d^{-5})(2c^{-5} d^4)$$ and find which option it matches. 2. **Write the formula and rules:** When multiplying expressions with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Multiply the coefficients:** $$10 \times 2 = 20$$. 4. **Multiply the variables with exponents:** $$c^6 \times c^{-5} = c^{6 + (-5)} = c^{1} = c$$ $$d^{-5} \times d^{4} = d^{-5 + 4} = d^{-1} = \frac{1}{d}$$ 5. **Combine all parts:** $$20 \times c \times \frac{1}{d} = \frac{20c}{d}$$ 6. **Answer:** The expression simplifies to $$\frac{20c}{d}$$ which corresponds to option A.