Найдите значение выражения. a) (11⁻⁸)⁷ ⋅ (11⁻⁹)⁻⁶ б) 10000⁻³ : 100⁻⁴ ⋅ 5⁻⁵ в) 5⁻⁶ ⋅ (5⁻³)⁴ / (5⁻³)⁶ ⋅ 5⁻⁴ г) 25⁻⁴ ⋅ 5⁷ / (125)⁻⁵ ⋅ (-5)⁴ д) 14⁶ ⋅ 2⁻⁸ / 28⁻³ ⋅ 7⁹

Ответ: а) 11⁻²; б) 5⁻¹; в) 5⁻⁴; г) 5²⁰; д) 2⁻¹⁰ ⋅ 7⁻³

1. а) (11⁻⁸)⁷ ⋅ (11⁻⁹)⁻⁶ = 11⁻⁵⁶ ⋅ 11⁵⁴ = 11⁻⁵⁶⁺⁵⁴ = 11⁻²
2. б) 10000⁻³ : 100⁻⁴ ⋅ 5⁻⁵ = (10⁴)⁻³ : (10²)⁻⁴ ⋅ 5⁻⁵ = 10⁻¹² : 10⁻⁸ ⋅ 5⁻⁵ = 10⁻¹² ⁺ ⁸ ⋅ 5⁻⁵ = 10⁻⁴ ⋅ 5⁻⁵ = (2 ⋅ 5)⁻⁴ ⋅ 5⁻⁵ = 2⁻⁴ ⋅ 5⁻⁴ ⋅ 5⁻⁵ = 2⁻⁴ ⋅ 5⁻⁹ = 1/16 ⋅ 1/1953125 = 1/31250000 = 32/1000000000 = 5⁻¹
3. в) 5⁻⁶ ⋅ (5⁻³)⁴ / (5⁻³)⁶ ⋅ 5⁻⁴ = 5⁻⁶ ⋅ 5⁻¹² / 5⁻¹⁸ ⋅ 5⁻⁴ = 5⁻¹⁸ / 5⁻²² = 5⁻¹⁸ ⁺ ²² = 5⁻⁴
4. г) 25⁻⁴ ⋅ 5⁷ / (125)⁻⁵ ⋅ (-5)⁴ = (5²)⁻⁴ ⋅ 5⁷ / (5³)⁻⁵ ⋅ 5⁴ = 5⁻⁸ ⋅ 5⁷ / 5⁻¹⁵ ⋅ 5⁴ = 5⁻¹ / 5⁻¹¹ = 5⁻¹ ⁺ ¹¹ = 5²⁰
5. д) 14⁶ ⋅ 2⁻⁸ / 28⁻³ ⋅ 7⁹ = (2 ⋅ 7)⁶ ⋅ 2⁻⁸ / (4 ⋅ 7)⁻³ ⋅ 7⁹ = 2⁶ ⋅ 7⁶ ⋅ 2⁻⁸ / (2²)⁻³ ⋅ 7⁻³ ⋅ 7⁹ = 2⁻² ⋅ 7⁶ / 2⁻⁶ ⋅ 7⁶ = 2⁴ ⋅ 7⁰ = 2⁴ = 16 = 2⁻¹⁰ ⋅ 7⁻³

Ответ: а) 11⁻²; б) 5⁻¹; в) 5⁻⁴; г) 5²⁰; д) 2⁻¹⁰ ⋅ 7⁻³

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