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

Выполните деление:

1) $$\frac{32a^5}{15y^8}:\frac{4a^3}{45y^4}$$;

2) $$\frac{16x^2y^8}{15m^4n^8}:\left(-\frac{8x^3y^5}{35m^6n^7}\right)$$;

3) $$54p^{10}n^{17}:\frac{27p^{12}n^{14}}{22a^6}$$;

4) $$\frac{72a^5b^4}{25y^8}:(24a^7b^9)$$;

5) $$\frac{7x^4y^{13}}{18m^2n^5}:\frac{35x^5y^8}{33m^4n^8}:\frac{11y^2n^9}{9xm^4}$$;

6) $$\left(-\frac{3m^2n^3}{4b^4}\right)^3:\left(-\frac{3m^3n}{4b^6}\right)^4$$.

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) $$\frac{16x^2y^8}{15m^4n^8}:\left(-\frac{8x^3y^5}{35m^6n^7}\right)=\frac{16x^2y^8}{15m^4n^8}\cdot\left(-\frac{35m^6n^7}{8x^3y^5}\right)=-\frac{16\cdot35}{15\cdot8}\cdot\frac{m^{6-4}n^{7-8}y^{8-5}}{x^{3-2}}=-\frac{14y^3m^2}{3nx}.$$

3) $$54p^{10}n^{17}:\frac{27p^{12}n^{14}}{22a^6}=54p^{10}n^{17}\cdot\frac{22a^6}{27p^{12}n^{14}}=\frac{54\cdot22}{27}\cdot a^6\cdot p^{10-12}\cdot n^{17-14}=44\frac{a^6n^3}{p^2}.$$

4) $$\frac{72a^5b^4}{25y^8}:(24a^7b^9)=\frac{72a^5b^4}{25y^8}\cdot\frac{1}{24a^7b^9}=\frac{72}{25\cdot24}\cdot\frac{1}{a^2b^5y^8}=\frac{3}{25a^2b^5y^8}.$$

5) $$\frac{7x^4y^{13}}{18m^2n^5}:\frac{35x^5y^8}{33m^4n^8}:\frac{11y^2n^9}{9xm^4}$$

$$=\frac{7x^4y^{13}}{18m^2n^5}\cdot\frac{33m^4n^8}{35x^5y^8}\cdot\frac{9xm^4}{11y^2n^9}=\frac{7\cdot33\cdot9}{18\cdot35\cdot11}\cdot\frac{m^{4+4-2}}{n^{5-8+9}}\cdot\frac{y^{13-8-2}}{x^{5-4-1}}=\frac{3y^3m^6}{10n^6}.$$

6) $$\left(-\frac{3m^2n^3}{4b^4}\right)^3:\left(-\frac{3m^3n}{4b^6}\right)^4$$

$$=-\frac{3^3m^6n^9}{4^3b^{12}}:\frac{3^4m^{12}n^4}{4^4b^{24}}=-\frac{3^3m^6n^9}{4^3b^{12}}\cdot\frac{4^4b^{24}}{3^4m^{12}n^4}=-\frac{4b^{12}n^5}{3m^6}.$$

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) $$-\frac{4b^{12}n^5}{3m^6}$$.