94. Вычислить: 1) 48⁰, 10⁻², (2/3)⁻¹, (0,3)⁻³, (−1,2)⁻², (2 1/4)⁻²; 2) ³√27, ⁴√81, ⁵√32, ⁶√(8²), ⁸√(16²), ³√(27²); 3) 8^(1/3), 27^(2/3), 10000^(1/4), 32^(2/5), 32^(−3/5), (27/64)^(2/3).

Question

Вопрос:

Accepted Answer

1) Используем правила a⁰ = 1, a⁻ⁿ = 1/aⁿ:

48⁰ = 1; 10⁻² = 1/100; (2/3)⁻¹ = 3/2; (0,3)⁻³ = 1000/27; (−1,2)⁻² = 25/36; (2 1/4)⁻² = (9/4)⁻² = 16/81.

2) ³√27 = 3; ⁴√81 = 3; ⁵√32 = 2; ⁶√(8²) = 2; ⁸√(16²) = √2; ³√(27²) = 9.

3) 8^(1/3) = 2; 27^(2/3) = 9; 10000^(1/4) = 10; 32^(2/5) = 4; 32^(−3/5) = 1/8; (27/64)^(2/3) = (3/4)² = 9/16.

Ответ: 1) 1; 1/100; 3/2; 1000/27; 25/36; 16/81. 2) 3; 3; 2; 2; √2; 9. 3) 2; 9; 10; 4; 1/8; 9/16.