985. Найдите значение выражения: a) 3⁻⁴ ⋅ 3⁶; б) 2⁴ : 2⁻³; в) 10⁸ ⋅ 10⁻⁵ ⋅ 10⁻⁶; г) 2¹⁰ : 2¹²; д) 5⁻⁸ : 5⁻³; e) 3⁻⁴ : 3; ж) (2⁻⁴)⁻¹; з) (5²)⁻² ⋅ 5³; и) 3⁻⁴ ⋅ (3⁻²)⁻⁴.

Решение:

• a) 3⁻⁴ ⋅ 3⁶ = 3⁻⁴⁺⁶ = 3² = 9
• б) 2⁴ : 2⁻³ = 2⁴⁻⁽⁻³⁾ = 2⁴⁺³ = 2⁷ = 128
• в) 10⁸ ⋅ 10⁻⁵ ⋅ 10⁻⁶ = 10⁸⁻⁵⁻⁶ = 10⁻³ = 0.001
• г) 2¹⁰ : 2¹² = 2¹⁰⁻¹² = 2⁻² = 1/4 = 0.25
• д) 5⁻⁸ : 5⁻³ = 5⁻⁸⁻⁽⁻³⁾ = 5⁻⁸⁺³ = 5⁻⁵ = 1/3125
• e) 3⁻⁴ : 3 = 3⁻⁴⁻¹ = 3⁻⁵ = 1/243
• ж) (2⁻⁴)⁻¹ = 2⁽⁻⁴⁾⋅⁽⁻¹⁾ = 2⁴ = 16
• з) (5²)⁻² ⋅ 5³ = 5²⋅⁽⁻²⁾ ⋅ 5³ = 5⁻⁴ ⋅ 5³ = 5⁻⁴⁺³ = 5⁻¹ = 1/5 = 0.2
• и) 3⁻⁴ ⋅ (3⁻²)⁻⁴ = 3⁻⁴ ⋅ 3⁽⁻²⁾⋅⁽⁻⁴⁾ = 3⁻⁴ ⋅ 3⁸ = 3⁻⁴⁺⁸ = 3⁴ = 81

Ответ: a) 9; б) 128; в) 0.001; г) 0.25; д) 1/3125; e) 1/243; ж) 16; з) 0.2; и) 81.