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36-[18-{14-(15-4-:2xx2)}]...

`36-[18-{14-(15-4-:2xx2)}]`

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To simplify the expression `36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]`, we will follow the BODMAS/BIDMAS rule, which stands for Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). ### Step-by-Step Solution: 1. **Identify and Solve the Innermost Bracket**: Start with the innermost round bracket: \[ (15 - 4 ÷ 2 × 2) \] According to BODMAS, we first perform the division and multiplication from left to right. - Calculate \(4 ÷ 2 = 2\) - Then, calculate \(2 × 2 = 4\) - Now substitute back into the expression: \[ 15 - 4 = 11 \] So, we have: \[ (15 - 4 ÷ 2 × 2) = 11 \] 2. **Substitute Back into the Curly Bracket**: Now substitute \(11\) back into the curly bracket: \[ {14 - (15 - 4 ÷ 2 × 2)} = {14 - 11} \] Calculate: \[ 14 - 11 = 3 \] 3. **Substitute Back into the Square Bracket**: Now substitute \(3\) back into the square bracket: \[ [18 - {14 - (15 - 4 ÷ 2 × 2)}] = [18 - 3] \] Calculate: \[ 18 - 3 = 15 \] 4. **Final Calculation**: Now substitute \(15\) back into the original expression: \[ 36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}] = 36 - 15 \] Calculate: \[ 36 - 15 = 21 \] Thus, the final answer is: \[ \boxed{21} \]
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