Răspuns:
= (5²ⁿ⁺¹⁵•7ⁿ⁺²)² = patrat perfect
Explicație pas cu pas:
35ⁿ⁺³• 7ⁿ⁺¹• 125ⁿ⁺⁹ = patrat perfect ?
35ⁿ⁺³ = (5•7)ⁿ⁺³ = (5•7)³•(5•7)ⁿ
7ⁿ⁺¹ = 7•7ⁿ
125ⁿ⁺⁹ = (5³)ⁿ⁺⁹ = 5³ⁿ⁺²⁷ = 5²⁷•5³ⁿ
35ⁿ⁺³• 7ⁿ⁺¹• 125ⁿ⁺⁹ = 5³•7³•5ⁿ •7ⁿ •7•7ⁿ•5²⁷•5³ⁿ =
= 5³⁺²⁷•5ⁿ⁺³ⁿ•7³⁺¹•7ⁿ⁺ⁿ = 5³⁰•5⁴ⁿ•7⁴•7²ⁿ =
= (5¹⁵•5²ⁿ•7²•7ⁿ)² = (5²ⁿ⁺¹⁵•7ⁿ⁺²)² = patrat perfect
