Explanation

The intended expression is (a⁸+a⁴+1)(b⁸+b⁴+1)/(a⁴b⁴) = (a⁴+1+1/a⁴)(b⁴+1+1/b⁴) (plain multiplication would have infimum 0). By AM ≥ GM, a⁴+1/a⁴ ≥ 2, so each bracket is ≥ 3, with equality at a = b = 1. The minimum is 3×3 = 9 — option C.