Вправи: 360 (1-2)

360. Знайдіть х. Подайте відповідь у вигляді степеня.

1) (15 • 8 • 40⁰)^–12 = x • 100^–6;

(120 • 1)^–12 = x • (10²)^–6;

(12 • 10)^–12 = x • 10^–12;

12^–12 • 10^–12 = x • 10^–12 |: 10^–12;

x = 12^–12.

2) (5 • 8)^–8 • (0,2^–2)⁴ = x^–1 • 4^–12;

40^–8 • (210)^–8 = x^–1 • 4^–12;

(40•210)^–8 = 4-12x;

8^–8 = 4-12x;

(2³)^–8 = (23)-12x;

2^–24 = 2-24x;

x = 1.

3) (0,375x)⁶ = (223)^–6;

(0,375x)⁶ = (83)^–6;

(0,375x)⁶ = (38)⁶;

0,375x = 38;

0,375x = 0,375;

x = 1.

4) 3,6^–10 = x • 4^–5 • 9^–10;

(3610)^–10 = x • (2²)^–5 • 9^–10;

(185)^–10 = x • 2^–10 • 9^–10;

18-105-10 = x • 18^–10 |: 18–10;

x = 15-10 = 5¹⁰.

5) (116)^–4 = x • 0,49^–2;

(76)^–4 = x • (49100)^–2;

(76)^–4 = x • ((710)²)^–2;

7-46-4 = x • 7-410-4 |: 7^–4;

6⁴ = x • 10⁴;

x = 6⁴ : 10⁴;

x = (610)⁴ = 0,6⁴.

6) x = 254• 0,5-410-2• 80 = (52)4•(12)-4(2•5)-2•1 = 58•24 2-2• 5-2 = 2⁶ • 5¹⁰ = (2³ • 5⁵)² = (8 • 3125)² = 25000².