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

1) (7^4)^5 :(7^9)^2 = 7^20 :7^18;
2) 8^6 :16^4 = (2^3)^6 :(2^4)^4;
3) (11^16·(11^7)^3)/(11^9)^4;
4) (36^3·216^2)/6^12;
5) (2^9·5^9)/10^6;
6) 4^19 ·0,25^17;
7) 18^6/(64·27^4);
8) 24^5/(4^7·9^2).

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.