Answer:
(7^9)/4 = 40,353,607/4
Explanation:
Assuming each digit is used once and exponentiation is allowed, the largest numerator and smallest denominator will result in the largest fraction.
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If other functions, such as factorial are allowed, then there might need to be a limit on the number of times they are applied. For example,
(7!)^(9!)/4 has about 1 million digits
something like ...
((7!)^(9!))!/4 has many more digits than that
and you can keep piling on the factorial symbols to any desired depth.