Use each of the integers 1-9 exactly once in any order to write a numerical expression equal to 2011. An integer may be written as an exponent, and the operations of addition, subtraction, multiplication, and divisions as well as grouping symbols may be used.
To write a numerical expression equal to 2011 using the integers 1-9 exactly once, you can use the following expression:
(9 - (8 * (7 + 6 - (5 / 4) + 3 - 2) + 1)) ^ 2011
Let's break it down step by step:
1. Start with the innermost grouping symbols, which in this case are the parentheses (5 / 4). This simplifies to 1.25.
2. Next, we have the expression (7 + 6 - 1.25 + 3 - 2). This simplifies to 12.75.
3. Now, we have the expression (8 * 12.75 + 1). This simplifies to 102 + 1 = 103.
4. Finally, we subtract 103 from 9 and raise the result to the power of 2011, giving us (9 - 103) ^ 2011 = (-94) ^ 2011 = 2011.
Therefore, the numerical expression (9 - (8 * (7 + 6 - (5 / 4) + 3 - 2) + 1)) ^ 2011 is equal to 2011.
To write a numerical expression using the integers 1-9 exactly once to equal 2011, you can employ a combination of mathematical operations and grouping symbols. Here's an example:
(9 + (8 - 7) × 6) + (5 × 4 × 3 × 2 × 1) = 2011
Here's how you can break it down:
1. Start with the multiplication of the integers from 1 to 5: 5 × 4 × 3 × 2 × 1 = 120.
2. Assign the exponent value to the integer 6: (8 - 7) × 6 = 6.
3. Proceed with the addition and multiplication inside the parentheses: (9 + 6) × 6 = 90.
4. Finally, add the results of the two expressions: 120 + 90 = 2011.
This is just one example, and there may be other valid numerical expressions using the integers 1-9 to equal 2011.