1. **State the problem:** Simplify the expression $$\frac{15 \times 4 - 3 + 8 \times 3}{\left[\frac{64}{8} + \left(\frac{36}{4} + 61\right) \div 7 \times 3 + \frac{25}{5} + 3 - 19\right]}$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)). 3. **Simplify numerator:** - Calculate $15 \times 4 = 60$ - Calculate $8 \times 3 = 24$ - Substitute: $60 - 3 + 24$ - Simplify: $60 - 3 = 57$, then $57 + 24 = 81$ 4. **Simplify denominator step-by-step:** - Calculate $\frac{64}{8} = 8$ - Calculate $\frac{36}{4} = 9$ - Add inside parentheses: $9 + 61 = 70$ - Divide and multiply: $70 \div 7 \times 3 = 10 \times 3 = 30$ - Calculate $\frac{25}{5} = 5$ - Substitute all: $8 + 30 + 5 + 3 - 19$ - Simplify stepwise: $8 + 30 = 38$, $38 + 5 = 43$, $43 + 3 = 46$, $46 - 19 = 27$ 5. **Final expression:** $$\frac{81}{27}$$ 6. **Simplify fraction:** $$\frac{81}{27} = 3$$ **Answer:** The value of the expression is $3$.