Factorial everywhere

Given: \[\large\frac{1! \times 2! \times 3! \times \dots \times 10! }{(1!)^2(3!)^2(5!)^2(7!)^2(9!)^2} = 15 \times 2^n\]

What is the value of \( n=?\)

Notation: \(!\) denotes the factorial notation; for example: \(8! = 1\times 2 \times 3 \times ... \times 8\).

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