1. **State the problem:** Simplify the expression: $$4 - \{6 + [-5 + (12 - 8)]\} - 5 + \{4 + [3 - (4 - 8) + (-5 - 10)]\} - [(8 + 3) - (5 - 1)] + [8 - 3) - (5 + 1)] + \{9 - [2 - (1 - 5)]\} - [4 - (5 - 4) + (-5)] + 2(7 - 4) + 3(1 - 5) + 8 - 4(2 - 3 - 1) + 2(8 - 5) + 3(4 - 5) + \sqrt{36} \times 1^6 + 5^3 \div 25 - \sqrt[3]{125} \times 2 + 810 \div 3^3 - 4 \times \sqrt[3]{27} - (2^8 - 3^5) + 2^2 + 1200 - [(4^4 - 2^8) + \sqrt{144} \times 84] + (2^3 + 3^4 + 4^5 - 10^3) - (\sqrt{121} \times 10) 2. **Use order of operations (PEMDAS):** Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). 3. **Simplify inside brackets and parentheses step-by-step:** - Calculate innermost parentheses: - $(12 - 8) = 4$ - $[-5 + 4] = -1$ - $6 + (-1) = 5$ - So, $4 - \{5\} = 4 - 5 = -1$ - Next bracket: - $(4 - 8) = -4$ - $(-5 - 10) = -15$ - $3 - (-4) + (-15) = 3 + 4 - 15 = -8$ - $4 + (-8) = -4$ - So, $-1 - 5 + (-4) = -1 - 5 - 4 = -10$ - Next bracket: - $(8 + 3) = 11$ - $(5 - 1) = 4$ - $11 - 4 = 7$ - $[8 - 3) - (5 + 1)]$ has mismatched bracket, assume it means $[8 - 3 - (5 + 1)]$ - $(5 + 1) = 6$ - $8 - 3 - 6 = -1$ - So, $-10 - 7 + (-1) = -10 - 7 - 1 = -18$ - Next bracket: - $(1 - 5) = -4$ - $2 - (-4) = 6$ - $9 - 6 = 3$ - $(5 - 4) = 1$ - $4 - 1 + (-5) = 4 - 1 - 5 = -2$ - So, $3 - (-2) = 3 + 2 = 5$ - Next terms: - $2(7 - 4) = 2 \times 3 = 6$ - $3(1 - 5) = 3 \times (-4) = -12$ - Sum: $6 - 12 + 8 = 2$ - Next terms: - $(2 - 3 - 1) = 2 - 3 - 1 = -2$ - $-4 \times (-2) = 8$ - $2(8 - 5) = 2 \times 3 = 6$ - $3(4 - 5) = 3 \times (-1) = -3$ - Sum: $8 + 6 - 3 = 11$ - Next terms: - $\sqrt{36} = 6$ - $1^6 = 1$ - $5^3 = 125$ - $125 \div 25 = 5$ - $\sqrt[3]{125} = 5$ - $5 \times 2 = 10$ - Sum: $6 \times 1 + 5 - 10 = 6 + 5 - 10 = 1$ - Next terms: - $3^3 = 27$ - $810 \div 27 = 30$ - $\sqrt[3]{27} = 3$ - $4 \times 3 = 12$ - $2^8 = 256$ - $3^5 = 243$ - $256 - 243 = 13$ - $2^2 = 4$ - Sum: $30 - 12 - 13 + 4 = 9$ - Next terms: - $4^4 = 256$ - $2^8 = 256$ - $256 - 256 = 0$ - $\sqrt{144} = 12$ - $12 \times 84 = 1008$ - Sum inside bracket: $0 + 1008 = 1008$ - $1200 - 1008 = 192$ - Next terms: - $2^3 = 8$ - $3^4 = 81$ - $4^5 = 1024$ - $10^3 = 1000$ - Sum: $8 + 81 + 1024 - 1000 = 113$ - $\sqrt{121} = 11$ - $11 \times 10 = 110$ - Sum: $113 - 110 = 3$ 4. **Add all simplified parts:** $$-18 + 5 + 2 + 11 + 1 + 9 + 192 + 3 = 205$$ **Final answer:** $$\boxed{205}$$