a) 2¹⁹×8¹⁷ = 2¹⁹×(2³)¹⁷ = 2¹⁹×2⁵¹ = 2⁷⁰ = (2³⁵)² = patrat perfect
b)3⁵×27¹¹ = 3⁵×(3³)¹¹ = 3⁵×3³³ = 3³⁸ = (3¹⁹)² = patrat perfect
c)2⁵×6¹¹×3⁷ = 2⁵×(2×3)¹¹×3⁷ = 2⁵×2¹¹×3¹¹×3⁷ = 2¹⁶×3¹⁸ = (2⁸×3⁹)² = patrat perfect
d)5⁴ⁿ⁺¹×125²ⁿ⁺³ = 5⁴ⁿ⁺¹×(5³)²ⁿ⁺³ = 5⁴ⁿ⁺¹×5⁶ⁿ⁺⁹ = 5¹⁰ⁿ⁺¹⁰ = (5⁵ⁿ⁺⁵)² = patrat perfect