Вправи

Вправи: 851

Алгебра, 8 клас · Вправи

Текстова відповідь

1) 25^–³ • 5⁸ = (5²)^–³ • 5⁸ = 5^–⁶ • 5⁸ = 5² = 25;

2) 64^–³ : 32^–³ = (2⁶)^–³ : (2⁵)^–³ = 2^–¹⁸ : 2^–¹⁵ = 2^–¹⁸^–⁽^–¹⁵⁾ = 2^–³ = 123 = 18;

3) 10^–¹⁰ : 1000^–³ • (0,001)^–⁵ = 10^–¹⁰ • (10³)^–³ • (10^–³)^–⁵ = 10^–¹⁰ : 10^–⁹ • 10¹⁵ = 10^–¹⁰⁺⁽^–⁹⁾⁺¹⁵ = 10⁴ = 1104 = 0,0001;

4) (-27)-12 • 9581-4 • 3-7 = (-33)-12• (32)5(34)-4 • 3-7 = 3-36• 3103-16• 3-7 = 3-263-23 = 3^–²⁶^–⁽^–²³⁾ = 3^–³ = 133 = 127;

5) 154 • 6-6 45-3 • 39 = (3 • 5)4 • 5-6(32 • 5)-3 • 39 = 34 • 54 • 5-63-6 • 5-3 • 39 = 34 • 5-233 • 5-3 = 3 • 51 = 15;

6) (0,125)-8• 16-732-2 = (1251000)-8 •(24)-7 (25)-2 = (128)-8• 2-28 2-10 = (2-3)-8• 2-292-10 = 224•2-28 2-10 = 2²⁴⁺⁽^–²⁸⁾^–⁽^–¹⁰⁾ = 2⁶ = 64.