Подготовка к ОГЭ Вариант 1 Вычислить: 1) (5^3)^(-4) / 5^(-11) 2) 5^(-7) * (5^5)^2 3) 5^(-3) * 5^(-9) / 5^(-12) 4) (6 * 10^2)^3 * (12 * 10^-4) 5) 7^(-9) * 7^12 / 7^4 6) (2^8)^(-1) / 2^-9 7) 3^-8 * (3^6)^2 8) 4^8 * 11^12 / 44^8

Решение:

1. \( \frac{(5^3)^{-4}}{5^{-11}} = \frac{5^{3 \times (-4)}}{5^{-11}} = \frac{5^{-12}}{5^{-11}} = 5^{-12 - (-11)} = 5^{-12 + 11} = 5^{-1} = \frac{1}{5} \)
2. \( 5^{-7} \times (5^5)^2 = 5^{-7} \times 5^{5 \times 2} = 5^{-7} \times 5^{10} = 5^{-7 + 10} = 5^3 = 125 \)
3. \( \frac{5^{-3} \times 5^{-9}}{5^{-12}} = \frac{5^{-3 + (-9)}}{5^{-12}} = \frac{5^{-12}}{5^{-12}} = 1 \)
4. \( (6 \times 10^2)^3 \times (12 \times 10^{-4}) = (6^3 \times (10^2)^3) \times (12 \times 10^{-4}) = (216 \times 10^6) \times (12 \times 10^{-4}) = 216 \times 12 \times 10^{6 + (-4)} = 2592 \times 10^2 = 259200 \)
5. \( \frac{7^{-9} \times 7^{12}}{7^4} = \frac{7^{-9 + 12}}{7^4} = \frac{7^3}{7^4} = 7^{3-4} = 7^{-1} = \frac{1}{7} \)
6. \( \frac{(2^8)^{-1}}{2^{-9}} = \frac{2^{8 \times (-1)}}{2^{-9}} = \frac{2^{-8}}{2^{-9}} = 2^{-8 - (-9)} = 2^{-8 + 9} = 2^1 = 2 \)
7. \( 3^{-8} \times (3^6)^2 = 3^{-8} \times 3^{6 \times 2} = 3^{-8} \times 3^{12} = 3^{-8 + 12} = 3^4 = 81 \)
8. \( \frac{4^8 \times 11^{12}}{44^8} = \frac{4^8 \times 11^{12}}{(4 \times 11)^8} = \frac{4^8 \times 11^{12}}{4^8 \times 11^8} = \frac{11^{12}}{11^8} = 11^{12-8} = 11^4 = 14641 \)

Ответ: 1) 1/5; 2) 125; 3) 1; 4) 259200; 5) 1/7; 6) 2; 7) 81; 8) 14641.