001. Упростите выражение и найдите его значение: a) 1,6x⁻¹y¹² ⋅ 5x³y⁻¹¹ при x = -0,2, y = 1/5; б) 6 x⁻³y³ ⋅ 30x³y⁻⁴ при x = 127, y = 1/5.

Краткое пояснение:

Пошаговое решение:

• a) 1,6x⁻¹y¹² ⋅ 5x³y⁻¹¹:
  Упрощаем выражение: (1,6 ⋅ 5) ⋅ (x⁻¹ ⋅ x³) ⋅ (y¹² ⋅ y⁻¹¹) = 8 ⋅ x² ⋅ y¹ = 8x²y.
  Подставляем значения: x = -0,2 = -1/5, y = 1/5.
  8x²y = 8 ⋅ (-1/5)² ⋅ (1/5) = 8 ⋅ (1/25) ⋅ (1/5) = 8/125.
• б) 6 x⁻³y³ ⋅ 30x³y⁻⁴:
  Упрощаем выражение: (6 ⋅ 30) ⋅ (x⁻³ ⋅ x³) ⋅ (y³ ⋅ y⁻⁴) = 180 ⋅ x⁰ ⋅ y⁻¹ = 180 ⋅ 1 ⋅ y⁻¹ = 180y⁻¹ = \( \frac{180}{y} \).
  Подставляем значение: y = 1/5.
  \( \frac{180}{y} \) = \( \frac{180}{\frac{1}{5}} \) = 180 ⋅ 5 = 900.

Ответ: а) 8/125, б) 900