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.