$$ 8 imes 9 - [ 32 - \{ 24 \div ( 8 - \overline { 4 - 2 } ) \} ] $$

Question

$$ 8 	imes 9 - [ 32 - \{ 24 \div ( 8 - \overline { 4 - 2 } ) \} ] $$

UpStudy AI · Accepted Answer

To solve the expression $$ 8 \times 9 - [ 32 - \{ 24 \div ( 8 - \overline { 4 - 2 } ) \} ] $$, we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).

1. **Calculate the innermost expression**: 
   $$
   4 - 2 = 2
   $$
   Therefore, $$ \overline{4 - 2} = 2 $$.

2. **Substitute back into the expression**:
   $$
   8 \times 9 - [ 32 - \{ 24 \div ( 8 - 2 ) \} ]
   $$

3. **Calculate $$ 8 - 2 $$**:
   $$
   8 - 2 = 6
   $$

4. **Substitute back into the expression**:
   $$
   8 \times 9 - [ 32 - \{ 24 \div 6 \} ]
   $$

5. **Calculate $$ 24 \div 6 $$**:
   $$
   24 \div 6 = 4
   $$

6. **Substitute back into the expression**:
   $$
   8 \times 9 - [ 32 - 4 ]
   $$

7. **Calculate $$ 32 - 4 $$**:
   $$
   32 - 4 = 28
   $$

8. **Substitute back into the expression**:
   $$
   8 \times 9 - 28
   $$

9. **Calculate $$ 8 \times 9 $$**:
   $$
   8 \times 9 = 72
   $$

10. **Substitute back into the expression**:
    $$
    72 - 28
    $$

11. **Calculate $$ 72 - 28 $$**:
    $$
    72 - 28 = 44
    $$

Thus, the final result is:
$$
\boxed{44}
$$
The final result is 44.

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