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There are a huge number of arithmetic, algebraic and trigonometric operators.
It works for some operators in arithmetic as it does in geometry, and not with other operators.
Usually, yes.
It could be. However, it is not possible to be sure since there are no operators between the numbers.
Using only the digits and the basic operators of arithmetic, 71. If other operators are allowed then 71! = 8.5*10101 approx, or 85 googol is one possible answer.