1. **State the problem:** Simplify the expression $$\frac{C^{5+4}}{C^2 \cdot C^{1-5}}$$. 2. **Use the laws of exponents:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the exponents in numerator and denominator:** - Numerator exponent: $$5+4=9$$ - Denominator exponents: $$2$$ and $$1-5 = -4$$ 4. **Combine the denominator terms using multiplication rule for exponents:** $$a^m \cdot a^n = a^{m+n}$$ $$C^2 \cdot C^{-4} = C^{2 + (-4)} = C^{-2}$$ 5. **Rewrite the original expression:** $$\frac{C^9}{C^{-2}}$$ 6. **Apply division rule for exponents:** $$C^{9 - (-2)} = C^{9 + 2} = C^{11}$$ 7. **Final answer:** $$\boxed{C^{11}}$$