А4. Упростите выражение: ((3x⁻²)/y⁻¹)⁻⁴ ⋅ 162x⁻⁷y⁴.

Пошаговое решение:

(((3x⁻²)/y⁻¹)⁻⁴) ⋅ 162x⁻⁷y⁴ = (3x⁻²/y⁻¹)⁻⁴ ⋅ 162x⁻⁷y⁴ = (3⁻⁴ ⋅ x⁸/y⁴) ⋅ 162x⁻⁷y⁴ = (1/81)⋅x⁸⋅y⁻⁴ ⋅ 162x⁻⁷y⁴ = (162/81) ⋅ x⁸⁻⁷ ⋅ y⁻⁴⁺⁴ = 2x¹y⁰ = 2x

Ответ: 2x