1. The problem asks to arrange the cards 9, 5, 6 and the operators (, ), x, + to create the calculation with the largest possible value. 2. The operators available are multiplication (x) and addition (+), and parentheses can be used to change the order of operations. 3. Multiplication has higher precedence than addition, but parentheses can override this. 4. To maximize the value, we want to multiply the largest numbers possible and add the remaining number. 5. The numbers are 9, 5, and 6. The largest product is 9 x 6 = 54. 6. Adding 5 to this product gives 54 + 5 = 59. 7. Using parentheses to ensure multiplication happens first: (9 x 6) + 5 = 59. 8. Other arrangements like 9 x (5 + 6) = 9 x 11 = 99 produce a larger value. 9. So the largest value is 99 with the expression 9 x (5 + 6). 10. Final answer: $$9 \times (5 + 6) = 9 \times 11 = 99$$