Using each number 2, 3, 4, 5 exactly once, and any of the operators + - * \ ^ any number of times:

  1. What expression yields the largest possible number?
  2. What expression yields the smallest (most negative) number?
  3. How close can you get to $e = 2.71828...$?
  4. What is the smallest positive integer you cannot construct?

Examples (These are not answers!):

  1. 2 3 4 5 * * * = 120
  2. 5 4 3 + - = -2
  3. 4 5 * 3 2 ^ / = 2.222
  4. 4 2 ^ 3 5 * - = 1