(2^4+1/4)(4^4+1/4)(6^4+1/4)/(1+1/4)(3^4+1/4)(5^4+1/4)

85

分子、分母同乘4^3，则原式化为：
(4·2^4＋1)(4·4^4＋1)(4·6^4＋1)/(4·1^4＋1)(4·3^4＋1)(4·5^4＋1)

∵4·n^4＋1＝(2·n^2－2n＋1)(2·n^2＋2n＋1)＝[2·n·(n－1)＋1][2·n·(n＋1)＋1]
∴原式＝[(2·2·1＋1)(2·2·3＋1)][(2·4·3＋1)(2·4·5＋1)][(2·6·5＋1)(2·6·7＋1)]
/[(2·1·0＋1)(2·1·2＋1)][(2·3·2＋1)(2·3·4＋1)][(2·5·4＋1)(2·5·6＋1)]
＝(2·6·7＋1)/(2·1·0＋1)＝85/1
＝85

85