1. **State the problem:** Simplify the expression $$\frac{6 + 4(7 + 4)}{5^3 + 9}$$. 2. **Apply the order of operations:** First, solve inside the parentheses. $$7 + 4 = 11$$ 3. **Multiply:** $$4 \times 11 = 44$$ 4. **Add in the numerator:** $$6 + 44 = 50$$ 5. **Calculate the denominator:** $$5^3 = 5 \times 5 \times 5 = 125$$ $$125 + 9 = 134$$ 6. **Write the fraction:** $$\frac{50}{134}$$ 7. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (2):** $$\frac{\cancel{50}^ {25}}{\cancel{134}^{67}}$$ 8. **Final simplified answer:** $$\frac{25}{67}$$