1. **State the problem:** Simplify the expression $$\frac{27h^2}{3h^9(11k + 6)}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Factor constants and simplify fractions. - Keep terms in parentheses as they are since they cannot be simplified further without more information. 3. **Simplify constants:** $$\frac{27}{3} = 9$$. 4. **Simplify powers of $h$:** $$\frac{h^2}{h^9} = h^{2-9} = h^{-7} = \frac{1}{h^7}$$. 5. **Rewrite the expression:** $$\frac{27h^2}{3h^9(11k + 6)} = \frac{9}{h^7(11k + 6)}$$. 6. **Final simplified form:** $$\boxed{\frac{9}{h^7(11k + 6)}}$$. This is the fully simplified expression because the numerator and denominator have no common factors left and the negative exponent is expressed as a positive exponent in the denominator.