Упр.7.33 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (6^4 )^4 :(6^5 )^3; 4) (?25^3•125^2)/5^10 ;
2) 8^3 :4^4; 5) (3^8•7^8)/?21^7 ;
3) (7^14•(7^2 )^3)/((7^3 )^6•7^2 ); 6) (5^9•4^6)/?20^6 .

1. $$\left(6^4\right)^4 : \left(6^5\right)^3 = 6^{16} : 6^{15} = 6^{16-15} = 6.$$
2. $$8^3 : 4^4 = \left(2^3\right)^3 : \left(2^2\right)^4 = 2^9 : 2^8 = 2^{9-8} = 2.$$
3. $$\frac{7^{14}\cdot \left(7^2\right)^3}{\left(7^3\right)^6\cdot 7^2} = \frac{7^{14}\cdot 7^6}{7^{18}\cdot 7^2} = \frac{7^{20}}{7^{20}} = 1.$$
4. $$\frac{25^3\cdot 125^2}{5^{10}} = \frac{(5^2)^3\cdot (5^3)^2}{5^{10}} = \frac{5^6\cdot 5^6}{5^{10}} = \frac{5^{12}}{5^{10}} = 5^2 = 25.$$
5. $$\frac{3^8\cdot 7^8}{21^7} = \frac{(3\cdot 7)^8}{21^7} = \frac{21^8}{21^7} = 21.$$
6. $$\frac{5^9\cdot 4^6}{20^6} = \frac{5^9\cdot 4^6}{(5\cdot 4)^6} = \frac{5^9\cdot 4^6}{5^6\cdot 4^6} = 5^3 = 125.$$

Ответ

1) 6; 2) 2; 3) 1; 4) 25; 5) 21; 6) 125.