3. a² ⋅ a³; a¹⁰ ⋅ a¹⁵; a⁶ ⋅ a⁴; a¹² ⋅ a⁵. a⁶ : a⁴; a¹⁰ : a³; a⁶ : a⁰; a¹¹ : a. (a²)²; (a³)²; (a⁴)⁵; (a⁰)². (2a²)²; (-2a³)³; (3a⁴)²; (-2a²b)⁴ ((x³)⁴ : x⁵)/x⁴ ((a⁴)⁵ ⋅ a¹⁰)/a⁶ (a⁵ : a⁰)/a³ ((n³)⁵ ⋅ (n²)³)/n⁵

Привет, ребята! Сейчас мы разберем упрощение выражений со степенями. * a² ⋅ a³ = a^(2+3) = a⁵ * a¹⁰ ⋅ a¹⁵ = a^(10+15) = a²⁵ * a⁶ ⋅ a⁴ = a^(6+4) = a¹⁰ * a¹² ⋅ a⁵ = a^(12+5) = a¹⁷ * a⁶ : a⁴ = a^(6-4) = a² * a¹⁰ : a³ = a^(10-3) = a⁷ * a⁶ : a⁰ = a⁶ (Помним, что a⁰ = 1, и деление на 1 не меняет значение) * a¹¹ : a = a¹¹ : a¹ = a^(11-1) = a¹⁰ * (a²)² = a^(2⋅2) = a⁴ * (a³)² = a^(3⋅2) = a⁶ * (a⁴)⁵ = a^(4⋅5) = a²⁰ * (a⁰)² = a^(0⋅2) = a⁰ = 1 * (2a²)² = 2² ⋅ (a²)² = 4 ⋅ a^(2⋅2) = 4a⁴ * (-2a³)³ = (-2)³ ⋅ (a³)^3 = -8 ⋅ a^(3⋅3) = -8a⁹ * (3a⁴)² = 3² ⋅ (a⁴)² = 9 ⋅ a^(4⋅2) = 9a⁸ * (-2a²b)⁴ = (-2)⁴ ⋅ (a²)⁴ ⋅ b⁴ = 16 ⋅ a^(2⋅4) ⋅ b⁴ = 16a⁸b⁴ * ((x³)⁴ : x⁵)/x⁴ = (x^(3*4) : x⁵) / x⁴ = (x¹² : x⁵) / x⁴ = x^(12-5) / x⁴ = x⁷ / x⁴ = x^(7-4) = x³ * ((a⁴)⁵ ⋅ a¹⁰)/a⁶ = (a^(4*5) * a¹⁰) / a⁶ = (a²⁰ * a¹⁰) / a⁶ = a^(20+10) / a⁶ = a³⁰ / a⁶ = a^(30-6) = a²⁴ * (a⁵ : a⁰)/a³ = (a⁵ / 1) / a³ = a⁵ / a³ = a^(5-3) = a² * ((n³)⁵ ⋅ (n²)³)/n⁵ = (n^(3*5) * n^(2*3)) / n⁵ = (n¹⁵ * n⁶) / n⁵ = n^(15+6) / n⁵ = n²¹ / n⁵ = n^(21-5) = n¹⁶ Помните основные правила работы со степенями! Если что-то осталось непонятным, спрашивайте.