Выполните действия (5a^3/11) ^4 + 4a^12/11

Выражение: (5*a^3/11) ^4+4*a^12/11

Ответ: (5949//14641) * a^12

Решаем по действиям:

1. 5/11 = (5//11)

2. ((5//11) * a^3) ^4 = (5//11) ^4*a^12

((5//11) * a^3) ^4 = (5//11) ^4*a^ (3*4)

2.1. 3*4=12

X3

_4_

12

3. (5//11) ^4=625//14641

4. 4/11 = (4//11)

5. (625//14641) * a^12 + (4//11) * a^12 = (5949//14641) * a^12

Решаем по шагам:

1. ((5//11) * a^3) ^4+4*a^12/11

1.1. 5/11 = (5//11)

2. (5//11) ^4*a^12+4*a^12/11

2.1. ((5//11) * a^3) ^4 = (5//11) ^4*a^12

((5//11) * a^3) ^4 = (5//11) ^4*a^ (3*4)

2.1.1. 3*4=12

X3

_4_

12

3. (625//14641) * a^12+4*a^12/11

3.1. (5//11) ^4=625//14641

4. (625//14641) * a^12 + (4//11) * a^12

4.1. 4/11 = (4//11)

5. (5949//14641) * a^12

5.1. (625//14641) * a^12 + (4//11) * a^12 = (5949//14641) * a^12

Приводим к окончательному ответу с возможной потерей точности:

Окончательный ответ: 0.4063*a^12

(5a^3/11) ^4 + 4a^12/11 = 625a^12/14641 + 4a^12/11 = a^12 (625/14641 + 4/11) =

= 5949/14641 a^12