To determine where parentheses can be placed in the expression [tex]\(6 + 2^3 - 4 \cdot 3\)[/tex] to make the value equal to 500, let's evaluate the different possible placements step-by-step.
We start with the given expression and try different placements of the parentheses:
1. [tex]\( (6 + 2^3) - 4 \cdot 3 \)[/tex]
- Calculate inside the parentheses first: [tex]\( 6 + 2^3 = 6 + 8 = 14 \)[/tex]
- Then multiply and subtract: [tex]\( 14 - 4 \cdot 3 = 14 - 12 = 2 \)[/tex]
- Final result: [tex]\( 2 \)[/tex]
2. [tex]\( 6 + (2^3 - 4) \cdot 3 \)[/tex]
- Calculate inside the parentheses: [tex]\( 2^3 - 4 = 8 - 4 = 4 \)[/tex]
- Then multiply and add: [tex]\( 6 + 4 \cdot 3 = 6 + 12 = 18 \)[/tex]
- Final result: [tex]\( 18 \)[/tex]
3. [tex]\( (6 + 2^3 - 4) \cdot 3 \)[/tex]
- Calculate inside the parentheses: [tex]\( 6 + 2^3 - 4 = 6 + 8 - 4 = 10 \)[/tex]
- Then multiply: [tex]\( 10 \cdot 3 = 30 \)[/tex]
- Final result: [tex]\( 30 \)[/tex]
4. [tex]\( 6 + ((2^3 - 4) \cdot 3) \)[/tex]
- Calculate inside the innermost parentheses: [tex]\( 2^3 - 4 = 8 - 4 = 4 \)[/tex]
- Then multiply: [tex]\( 4 \cdot 3 = 12 \)[/tex]
- Then add: [tex]\( 6 + 12 = 18 \)[/tex]
- Final result: [tex]\( 18 \)[/tex]
None of these parentheses placements resulted in 500. Therefore, it is not possible to place parentheses in the given expression to get a value of 500.
