Factorial everywhere

Given: 1!×2!×3!××10!(1!)2(3!)2(5!)2(7!)2(9!)2=15×2n\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=? n=?

Notation: !! denotes the factorial notation; for example: 8!=1×2×3×...×88! = 1\times 2 \times 3 \times ... \times 8.

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