Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаУпростите выражение: Вариант 1 1) 6x⁻⁵y⁷ ⋅ 2,5x⁷y⁻⁶; 3) 13x⁻⁴y / 52x⁻⁵y⁻⁶; 2) 3,2a⁶b : (0,8a⁻³b⁻³); 4) (9m⁻³/5n⁻¹)⁻² ⋅ 81m⁻⁶n³ Вариант 2 Упростите выражение: 1) 2,2a⁻⁸b⁵ ⋅ 5a¹⁰b⁻⁴; 3) 14a b⁻² / b⁻³ 56a⁻⁴; 2) 2,8m⁸n : (0,7m⁴n⁻²); 4) (5x⁻²/6y⁻¹)⁻³ ⋅ 125x⁻⁶y⁵.
Ответ:
Вариант 1
1)
6x⁻⁵y⁷ ⋅ 2,5x⁷y⁻⁶ = (6 ⋅ 2,5) ⋅ (x⁻⁵ ⋅ x⁷) ⋅ (y⁷ ⋅ y⁻⁶) = 15 ⋅ x⁽⁻⁵ ⁺ ⁷⁾ ⋅ y⁽⁷ ⁻ ⁶⁾ = 15x²y
2)
3,2a⁶b : (0,8a⁻³b⁻³) = \frac{3,2a⁶b}{0,8a⁻³b⁻³} = \frac{3,2}{0,8} ⋅ \frac{a⁶}{a⁻³} ⋅ \frac{b}{b⁻³} = 4 ⋅ a⁽⁶ ⁻ ⁽⁻³⁾⁾ ⋅ b⁽¹ ⁻ ⁽⁻³⁾⁾ = 4a⁹b⁴
3)
\frac{13x⁻⁴y}{52x⁻⁵y⁻⁶} = \frac{13}{52} ⋅ \frac{x⁻⁴}{x⁻⁵} ⋅ \frac{y}{y⁻⁶} = \frac{1}{4} ⋅ x⁽⁻⁴ ⁻ ⁽⁻⁵⁾⁾ ⋅ y⁽¹ ⁻ ⁽⁻⁶⁾⁾ = \frac{1}{4}xy⁷
4)
\left(\frac{9m⁻³}{5n⁻¹}\right)⁻² ⋅ 81m⁻⁶n³ = \left(\frac{5n⁻¹}{9m⁻³}\right)² ⋅ 81m⁻⁶n³ = \frac{25n⁻²}{81m⁻⁶} ⋅ 81m⁻⁶n³ = 25 ⋅ \frac{n⁻²}{1} ⋅ \frac{n³}{1} ⋅ \frac{m⁻⁶}{m⁻⁶} = 25n
Вариант 2
1)
2,2a⁻⁸b⁵ ⋅ 5a¹⁰b⁻⁴ = (2,2 ⋅ 5) ⋅ (a⁻⁸ ⋅ a¹⁰) ⋅ (b⁵ ⋅ b⁻⁴) = 11 ⋅ a⁽⁻⁸ ⁺ ¹⁰⁾ ⋅ b⁽⁵ ⁻ ⁴⁾ = 11a²b
2)
2,8m⁸n : (0,7m⁴n⁻²) = \frac{2,8m⁸n}{0,7m⁴n⁻²} = \frac{2,8}{0,7} ⋅ \frac{m⁸}{m⁴} ⋅ \frac{n}{n⁻²} = 4 ⋅ m⁽⁸ ⁻ ⁴⁾ ⋅ n⁽¹ ⁻ ⁽⁻²⁾⁾ = 4m⁴n³
3)
\frac{14a b⁻²}{b⁻³ 56a⁻⁴} = \frac{14}{56} ⋅ \frac{a}{a⁻⁴} ⋅ \frac{b⁻²}{b⁻³} = \frac{1}{4} ⋅ a⁽¹ ⁻ ⁽⁻⁴⁾⁾ ⋅ b⁽⁻² ⁻ ⁽⁻³⁾⁾ = \frac{1}{4}a⁵b
4)
\left(\frac{5x⁻²}{6y⁻¹}\right)⁻³ ⋅ 125x⁻⁶y⁵ = \left(\frac{6y⁻¹}{5x⁻²}\right)³ ⋅ 125x⁻⁶y⁵ = \frac{216y⁻³}{125x⁻⁶} ⋅ 125x⁻⁶y⁵ = 216 ⋅ \frac{y⁻³}{1} ⋅ \frac{y⁵}{1} ⋅ \frac{x⁻⁶}{x⁻⁶} = 216y²
