1. **State the problem:** Simplify the expression $$\frac{c^{-3} d^{5}}{c^{2} d^{-1}}$$. 2. **Recall the laws of exponents:** - When dividing like bases, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$. - Negative exponents mean reciprocal: $$a^{-m} = \frac{1}{a^{m}}$$. 3. **Apply the exponent rule to the base $c$:** $$c^{-3} \div c^{2} = c^{-3-2} = c^{-5}$$. 4. **Apply the exponent rule to the base $d$:** $$d^{5} \div d^{-1} = d^{5 - (-1)} = d^{5+1} = d^{6}$$. 5. **Combine the results:** $$\frac{c^{-3} d^{5}}{c^{2} d^{-1}} = c^{-5} d^{6}$$. 6. **Rewrite negative exponent as reciprocal:** $$c^{-5} = \frac{1}{c^{5}}$$. 7. **Final simplified expression:** $$\frac{d^{6}}{c^{5}}$$. This means the original expression simplifies to $$\frac{d^{6}}{c^{5}}$$.