3. Упростите выражение: 1) a) 6x⁻⁵y⁷⋅2,5xy⁻⁶; 2) a) 3,2a²b⁶:(0,8a³b⁻³); 3) a) \(\frac{13x⁻⁴}{y⁻⁶} \) : \(\frac{y}{52x⁻⁵} \); 4) a) (\(\frac{9m⁻³}{5n⁻¹} \))⁻²⋅81m⁻⁶n³; 6) 0,8a⁻⁶b⁴⋅5a¹²b⁻⁴; 6) \(\frac{3}{2} \)m⁻¹n⁻⁷:(-\(\frac{7}{8} \)m⁻⁵n⁻⁷); 6) \(\frac{21a⁻⁴}{10b⁻³} \) : \(\frac{5b⁻⁶}{7a⁻⁸} \); 6) (\(\frac{2x⁴}{y⁹} \))⁻³⋅(x⁻²y)⁻⁶.

3. Упростите выражение:

1. a) 6x⁻⁵y⁷⋅2,5xy⁻⁶

   Разбираемся: 6 ⋅ 2,5 ⋅ x⁽⁻⁵⁺¹⁾ ⋅ y⁽⁷⁻⁶⁾ = 15x⁻⁴y¹ = \(\frac{15y}{x⁴} \).

2. a) 3,2a²b⁶:(0,8a³b⁻³)

   Смотри, как это работает: \(\frac{3,2}{0,8} \) ⋅ a⁽²⁻³⁾ ⋅ b⁽⁶⁻⁽⁻³⁾⁾ = 4a⁻¹b⁹ = \(\frac{4b⁹}{a} \).

3. a) \(\frac{13x⁻⁴}{y⁻⁶} \) : \(\frac{y}{52x⁻⁵} \)

   Логика такая: \(\frac{13x⁻⁴}{y⁻⁶} \) ⋅ \(\frac{52x⁻⁵}{y} \) = \(\frac{13 ⋅ 52 ⋅ x⁽⁻⁴⁻⁵⁾}{y⁽⁻⁶⁺¹⁾} = \frac{676x⁻⁹}{y⁻⁵} = \frac{676y⁵}{x⁹} \).

4. a) (\(\frac{9m⁻³}{5n⁻¹} \))⁻²⋅81m⁻⁶n³

   Смотри, как это работает: (\(\frac{9m⁻³}{5n⁻¹} \))⁻² ⋅ 81m⁻⁶n³ = \(\frac{9⁻²m⁶}{5⁻²n⁻²} \) ⋅ 81m⁻⁶n³ = \(\frac{5²n² ⋅ 81n³}{9²m⁶ ⋅ m⁶} = \frac{25 ⋅ 81 ⋅ n⁵}{81 ⋅ m¹²} = \frac{25n⁵}{m¹²} \).

5. б) 0,8a⁻⁶b⁴⋅5a¹²b⁻⁴

   0, 8 ⋅ 5 ⋅ a⁽⁻⁶⁺¹²⁾ ⋅ b⁽⁴⁻⁴⁾ = 4a⁶b⁰ = 4a⁶.

6. б) \(\frac{3}{2} \)m⁻¹n⁻⁷:(-\(\frac{7}{8} \)m⁻⁵n⁻⁷)

   Разбираемся: \(\frac{3}{2} \) : (-\(\frac{7}{8} \)) ⋅ m⁽⁻¹⁻⁽⁻⁵⁾⁾ ⋅ n⁽⁻⁷⁻⁽⁻⁷⁾⁾ = -\(\frac{3}{2} \) ⋅ \(\frac{8}{7} \) ⋅ m⁴ ⋅ n⁰ = -\(\frac{12}{7} \)m⁴.

7. б) \(\frac{21a⁻⁴}{10b⁻³} \) : \(\frac{5b⁻⁶}{7a⁻⁸} \)

   Логика такая: \(\frac{21a⁻⁴}{10b⁻³} \) ⋅ \(\frac{7a⁻⁸}{5b⁻⁶} \) = \(\frac{21 ⋅ 7 ⋅ a⁽⁻⁴⁺⁸⁾}{10 ⋅ 5 ⋅ b⁽⁻³⁺⁶⁾} = \frac{147a⁴}{50b³} \).

8. б) (\(\frac{2x⁴}{y⁹} \))⁻³⋅(x⁻²y)⁻⁶

   Разбираемся: (\(\frac{2x⁴}{y⁹} \))⁻³ ⋅ (x⁻²y)⁻⁶ = \(\frac{2⁻³x⁻¹²}{y⁻²⁷} \) ⋅ x¹²y⁻⁶ = \(\frac{x⁰}{2³y⁽⁶⁺²⁷⁾} = \frac{1}{8y³³} \).