Ответ:

В решении.

Пошаговое объяснение:

8.

а) 25*5³*5⁰ = 5²*5³*5⁰ = 5²⁺³⁺⁰ = 5⁵;

b) 1/81 * 1/9 * (1/3)⁷ = 1/3⁴ * 1/3² * 1/3⁷ = 1/3⁴⁺²⁺⁷ = 1/3¹³ = 3⁻¹³;

с) (9 * 3⁹ * 27)/(3⁷ : 3⁴) =

= (3² * 3⁹ * 3³)/3⁷⁻⁴ =

= 3²⁺⁹⁺³/3³ = 3¹⁴/3³ = 3¹⁴⁻³ = 3¹¹;

d) (7¹¹ : 49)/(7⁴ * 7³) =

= (7¹¹ : 7²)/7⁴⁻³ =

= 7¹¹⁻²/7 = 7⁹/7 = 7⁹⁻¹ = 7⁸.

10.

а) (1000 - (-10)⁸)/10⁹ =

= (1000 - 100 000 000)/10⁹ =

= 99 999 000/10⁹ =

= 0,099 999 * 10⁹/10⁹ = 0,099999;

b) 81 * (-3)⁵ * (-27) =

= (-3)⁴ * (-3)⁵ * (-3)³ =

= (-3)⁴⁺⁵⁺³ = (-3)¹²;

с) (-1/32) * 1/16 * (1/2)⁶ =

= (-1/2)⁵ * (1/2)⁴ * (1/2)⁶ =

= -1/2⁵ * 1/2⁴ * 1/2⁶ =

= -1/2⁵⁺⁴⁺⁶ = -1/2¹⁵;

d) (36 * (-6)⁷ * (-6)⁸)/(6¹⁴ : (-6)) =

= ((-6)² * (-6)⁷ * (-6)⁸)/(-6)¹³ =

= (-6)²⁺⁷⁺⁸/(-6)¹³ =

= (-6)¹⁷/(-6)¹³ = (-6)¹⁷⁻¹³ = (-6)⁴.

12.

64³ = (2⁶)³ = 2¹⁸;

27⁵ = (3³)⁵ = 3¹⁵;

32⁵ = (2⁵)⁵ = 2²⁵;

9⁹ = (3²)⁹ = 3¹⁸;

25¹¹ = (5²)¹¹ = 5²²;

125⁷ = (5³)⁷ = 5²¹;

16⁹ = (2⁴)⁹ = 2³⁶.