Упр.31 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

Выполните деление:

1. $$\frac{16x^3}{9y^4}:\frac{8x^8}{27y^6}$$
2. $$\frac{18m^3n^4}{25p^6q^{10}}:\left(-\frac{4m^2n^9}{75p^5q^{12}}\right)$$
3. $$28a^{18}b^{19}:\frac{14a^{20}b^{15}}{15c^4}$$
4. $$\frac{48x^4y^3}{49z^9}:(16x^7y^8)$$
5. $$\frac{11a^5b^{12}}{12cd^6}:\frac{55a^3b^2}{18c^7d^4}:\frac{21b^6d^2}{20a^7c^3}$$
6. $$\left(-\frac{2p^4q^2}{5m^8}\right)^3:\left(-\frac{2p^5q^3}{5m^6}\right)^4$$

1. $$\frac{16x^3}{9y^4}:\frac{8x^8}{27y^6}=\frac{16x^3}{9y^4}\cdot\frac{27y^6}{8x^8}=\frac{16\cdot27}{9\cdot8}\cdot\frac{y^2}{x^5}=\frac{6y^2}{x^5}.$$

2. $$\frac{18m^3n^4}{25p^6q^{10}}:\left(-\frac{4m^2n^9}{75p^5q^{12}}\right)=-\frac{18m^3n^4}{25p^6q^{10}}\cdot\frac{75p^5q^{12}}{4m^2n^9}=-\frac{18\cdot75}{25\cdot4}\cdot\frac{mq^2}{pn^5}=-\frac{27mq^2}{2pn^5}.$$

3. $$28a^{18}b^{19}:\frac{14a^{20}b^{15}}{15c^4}=28a^{18}b^{19}\cdot\frac{15c^4}{14a^{20}b^{15}}=2\cdot15\cdot\frac{b^4c^4}{a^2}=\frac{30b^4c^4}{a^2}.$$

4. $$\frac{48x^4y^3}{49z^9}:(16x^7y^8)=\frac{48x^4y^3}{49z^9\cdot16x^7y^8}=\frac{3}{49x^3y^5z^9}.$$

5. $$\frac{11a^5b^{12}}{12cd^6}:\frac{55a^3b^2}{18c^7d^4}:\frac{21b^6d^2}{20a^7c^3}$$
   $$=\frac{11a^5b^{12}}{12cd^6}\cdot\frac{18c^7d^4}{55a^3b^2}\cdot\frac{20a^7c^3}{21b^6d^2}$$
   $$=\frac{11\cdot18\cdot20}{12\cdot55\cdot21}\cdot a^9b^4c^9\cdot\frac{1}{d^4}=\frac{2a^9b^4c^9}{7d^4}.$$

6. $$\left(-\frac{2p^4q^2}{5m^8}\right)^3:\left(-\frac{2p^5q^3}{5m^6}\right)^4$$
   $$=-\frac{8p^{12}q^6}{125m^{24}}:\frac{16p^{20}q^{12}}{625m^{24}}$$
   $$=-\frac{8p^{12}q^6}{125m^{24}}\cdot\frac{625m^{24}}{16p^{20}q^{12}}=-\frac{5}{2p^8q^6}.$$