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

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

1. $$\frac{16x^3}{9y^4}:\frac{8x^8}{27y^6}=\frac{16x^3}{9y^4}\cdot\frac{27y^6}{8x^8}$$
   $$=\frac{16\cdot 27}{9\cdot 8}\cdot\frac{x^3}{x^8}\cdot\frac{y^6}{y^4}=6\cdot\frac{1}{x^5}\cdot y^2=\frac{6y^2}{x^5}.$$
2. $$\frac{18m^3n^4}{25p^6q^{10}}:\left(-\frac{4m^2n^9}{75p^5q^{12}}\right)=\frac{18m^3n^4}{25p^6q^{10}}\cdot\frac{75p^5q^{12}}{-4m^2n^9}$$
   $$=-\frac{18\cdot 75}{25\cdot 4}\cdot\frac{m^3}{m^2}\cdot\frac{n^4}{n^9}\cdot\frac{p^5}{p^6}\cdot\frac{q^{12}}{q^{10}}$$
   $$=-\frac{27mq^2}{2n^5p}.$$
3. $$28a^{18}b^{19}:\frac{14a^{20}b^{15}}{15c^4}=28a^{18}b^{19}\cdot\frac{15c^4}{14a^{20}b^{15}}$$
   $$=\frac{28\cdot 15}{14}\cdot\frac{a^{18}}{a^{20}}\cdot\frac{b^{19}}{b^{15}}\cdot c^4 =30\cdot\frac{b^4c^4}{a^2}.$$
4. $$\frac{48x^4y^3}{49z^9}:(16x^7y^8)=\frac{48x^4y^3}{49z^9\cdot 16x^7y^8}$$
   $$=\frac{48}{49\cdot 16}\cdot\frac{x^4}{x^7}\cdot\frac{y^3}{y^8}\cdot\frac{1}{z^9} =\frac{3}{49x^3y^5z^9}.$$
5. $$\frac{11a^5b^{12}}{12cd^6}:\frac{55a^3b^2}{18c^7d^4}:\frac{21b^6d^2}{20a^7c^3}$$
   $$=\frac{11a^5b^{12}}{12cd^6}\cdot\frac{18c^7d^4}{55a^3b^2}\cdot\frac{20a^7c^3}{21b^6d^2}$$
   $$=\frac{11\cdot 18\cdot 20}{12\cdot 55\cdot 21}\cdot a^{5-3+7}\cdot b^{12-2-6}\cdot c^{7-1+3}\cdot d^{4-6-2}$$
   $$=\frac{2a^9b^4c^9}{7d^4}.$$
6. $$\left(-\frac{2p^4q^2}{5m^8}\right)^3:\left(-\frac{2p^5q^3}{5m^6}\right)^4$$
   $$=-\frac{8p^{12}q^6}{125m^{24}}:\frac{16p^{20}q^{12}}{625m^{24}}$$
   $$=-\frac{8p^{12}q^6}{125m^{24}}\cdot\frac{625m^{24}}{16p^{20}q^{12}}$$
   $$=-\frac{5}{2p^8q^6}.$$

Ответ

1) $$\frac{6y^2}{x^5}$$;
2) $$-\frac{27mq^2}{2n^5p}$$;
3) $$\frac{30b^4c^4}{a^2}$$;
4) $$\frac{3}{49x^3y^5z^9}$$;
5) $$\frac{2a^9b^4c^9}{7d^4}$$;
6) $$-\frac{5}{2p^8q^6}$$.