Упр.31 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (32a^5)/(15y^8 ) :(4a^3)/(45y^4);
2) (16x^2 y^8)/(15m^4 n^8 ) :(-(8x^3 y^5)/(35m^6 n^7 ));
3) 54p^10 n^17 :(27p^12 n^14)/(22a^6);
4) (72a^5 b^4)/(25y^8 ) :(24a^7 b^9);
5) (7x^4 y^13)/(18m^2 n^5 ) :(35x^5 y^8)/(33m^4 n^8 ) :(11y^2 n^9)/(9xm^4);
6) (-(3m^2 n^3)/(4b^4 ))^3 :(-(3m^3 n)/(4b^6 ))^4.

1. $$\frac{32a^5}{15y^8}:\frac{4a^3}{45y^4}=\frac{32a^5}{15y^8}\cdot\frac{45y^4}{4a^3}$$
   $$=\frac{32\cdot45}{15\cdot4}\cdot a^{5-3}\cdot y^{4-8}=24\frac{a^2}{y^4}$$
2. $$\frac{16x^2y^8}{15m^4n^8}:\left(-\frac{8x^3y^5}{35m^6n^7}\right)=\frac{16x^2y^8}{15m^4n^8}\cdot\left(-\frac{35m^6n^7}{8x^3y^5}\right)$$
   $$=-\frac{16\cdot35}{15\cdot8}\cdot x^{2-3}\cdot y^{8-5}\cdot m^{6-4}\cdot n^{7-8}$$
   $$=-\frac{14y^3m^2}{3nx}$$
3. $$54p^{10}n^{17}:\frac{27p^{12}n^{14}}{22a^6}=54p^{10}n^{17}\cdot\frac{22a^6}{27p^{12}n^{14}}$$
   $$=\frac{54\cdot22}{27}\cdot a^6\cdot p^{10-12}\cdot n^{17-14}=\frac{44a^6n^3}{p^2}$$
4. $$\frac{72a^5b^4}{25y^8}:(24a^7b^9)=\frac{72a^5b^4}{25y^8}\cdot\frac{1}{24a^7b^9}$$
   $$=\frac{72}{25\cdot24}\cdot a^{5-7}\cdot b^{4-9}\cdot \frac{1}{y^8}=\frac{3}{25a^2b^5y^8}$$
5. $$\frac{7x^4y^{13}}{18m^2n^5}:\frac{35x^5y^8}{33m^4n^8}:\frac{11y^2n^9}{9xm^4}$$
   $$=\frac{7x^4y^{13}}{18m^2n^5}\cdot\frac{33m^4n^8}{35x^5y^8}\cdot\frac{9xm^4}{11y^2n^9}$$
   $$=\frac{7\cdot33\cdot9}{18\cdot35\cdot11}\cdot x^{4-5+1}\cdot y^{13-8-2}\cdot m^{4-2+4}\cdot n^{8-5-9}$$
   $$=\frac{3y^3m^6}{10n^6}$$
6. $$\left(-\frac{3m^2n^3}{4b^4}\right)^3:\left(-\frac{3m^3n}{4b^6}\right)^4$$
   $$=-\frac{27m^6n^9}{64b^{12}}:\frac{81m^{12}n^4}{256b^{24}}$$
   $$=-\frac{27m^6n^9}{64b^{12}}\cdot\frac{256b^{24}}{81m^{12}n^4}$$
   $$=-\frac{4b^{12}n^5}{3m^6}$$

Ответ

1) $$\frac{24a^2}{y^4}$$;
2) $$-\frac{14y^3m^2}{3nx}$$;
3) $$\frac{44a^6n^3}{p^2}$$;
4) $$\frac{3}{25a^2b^5y^8}$$;
5) $$\frac{3y^3m^6}{10n^6}$$;
6) $$-\frac{4b^{12}n^5}{3m^6}$$.