Задание 12 Параграф 6 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 7 класс (Алгебра)

1. $$\left(7^4\right)^5 : \left(7^9\right)^2 = 7^{20} : 7^{18} = 7^2 = 49$$
2. $$8^6 : 16^4 = \left(2^3\right)^6 : \left(2^4\right)^4 = 2^{18} : 2^{16} = 2^2 = 4$$
3. $$\frac{11^{16}\cdot \left(11^7\right)^3}{\left(11^9\right)^4} = \frac{11^{16}\cdot 11^{21}}{11^{36}} = \frac{11^{37}}{11^{36}} = 11$$
4. $$\frac{36^3\cdot 216^2}{6^{12}} = \frac{\left(6^2\right)^3\cdot \left(6^3\right)^2}{6^{12}} = \frac{6^6\cdot 6^6}{6^{12}} = \frac{6^{12}}{6^{12}} = 1$$
5. $$\frac{2^9\cdot 5^9}{10^6} = \frac{(2\cdot 5)^9}{10^6} = \frac{10^9}{10^6} = 10^3 = 1000$$
6. $$4^{19}\cdot 0{,}25^{17} = 4^2\cdot 4^{17}\cdot 0{,}25^{17} = 16\cdot (4\cdot 0{,}25)^{17} = 16\cdot 1^{17} = 16$$
7. $$\frac{18^6}{64\cdot 27^4} = \frac{(2\cdot 3^2)^6}{2^6\cdot (3^3)^4} = \frac{2^6\cdot 3^{12}}{2^6\cdot 3^{12}} = 1$$
8. $$\frac{24^5}{4^7\cdot 9^2} = \frac{(2^3\cdot 3)^5}{(2^2)^7\cdot (3^2)^2} = \frac{2^{15}\cdot 3^5}{2^{14}\cdot 3^4} = 2\cdot 3 = 6$$

Ответ

1) 49; 2) 4; 3) 11; 4) 1; 5) 1000; 6) 16; 7) 1; 8) 6.