Упр.7.18 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) 2^3•2^4; 2) (3^2 )^3; 3) 0,2•0,2^2•0,2^3;
4) 0,5^12•2^12; 5) 2^12 :2^8; 6) (3^4 )^5 :3^19;
7) (1/3)^9•9^9; 8) 2,5^5•40^5.

1. $$2^3 \cdot 2^4 = 2^{3+4} = 2^7 = 128.$$
2. $$\left(3^2\right)^3 = 3^{2\cdot 3} = 3^6 = 729.$$
3. $$0{,}2 \cdot 0{,}2^2 \cdot 0{,}2^3 = 0{,}2^{1+2+3} = 0{,}2^6 = 0{,}000064.$$
4. $$0{,}5^{12} \cdot 2^{12} = (0{,}5 \cdot 2)^{12} = 1^{12} = 1.$$
5. $$2^{12} : 2^8 = 2^{12-8} = 2^4 = 16.$$
6. $$ \left(3^4\right)^5 : 3^{19} = 3^{20} : 3^{19} = 3^{20-19} = 3^1 = 3. $$
7. $$ \left(\frac13\right)^9 \cdot 9^9 = \left(\frac13 \cdot 9\right)^9 = 3^9 = 19683. $$
8. $$ 2{,}5^5 \cdot 40^5 = (2{,}5 \cdot 40)^5 = 100^5 = 10\,000\,000\,000. $$

Ответ

1) 128; 2) 729; 3) 0,000064; 4) 1; 5) 16; 6) 3; 7) 19683; 8) 10 000 000 000.