How exactly does (a4+4)(a^4 + 4) help?

Algebra Level 5

(24+14)(44+14)(1984+14)(2004+14)(14+14)(34+14)(1974+14)(1994+14)=?\large{\frac{\bigg(2^4 + \frac14\bigg)\bigg(4^4 + \frac14\bigg)\ldots\bigg(198^4 + \frac14\bigg)\bigg(200^4 + \frac14\bigg)}{\bigg(1^4 + \frac14\bigg)\bigg(3^4 + \frac14\bigg)\ldots\bigg(197^4 + \frac14\bigg)\bigg(199^4 + \frac14\bigg)} = ?}

HINT: Write the expression (a4+4)(a^4 + 4) as a product of two factors, where each one of those factors is equal to a sum of two squares.

Bonus: Simpify the following product.k=1n(2k)4+14(2k1)4+14\large{\displaystyle \prod_{k=1}^n \frac{(2k)^4+\frac14}{(2k-1)^4+\frac14}}

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