Упр.31 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

Выполните деление:

1. $$\frac{21b^8}{10c^6}:\frac{7b^2}{30c^3}$$;
2. $$\frac{40a^5b^9}{39c^6d^{14}}:\left(-\frac{5a^8b^3}{26c^{12}d^7}\right)$$;
3. $$36x^{16}y^{14}:\frac{18x^{18}y^{10}}{11m^3}$$;
4. $$\frac{60m^6n^5}{17p^4}:15m^8n^{10}$$;
5. $$\frac{17a^6b^{10}}{16c^2d^5}:\frac{34a^4b^4}{24c^6d^6}:\frac{15b^8d^4}{8a^8c^3}$$;
6. $$\left(-\frac{9x^5y^2}{7z^4}\right)^3:\left(-\frac{9x^4y^{10}}{7z^3}\right)^4$$.

1) $$\frac{21b^8}{10c^6}:\frac{7b^2}{30c^3}=\frac{21b^8}{10c^6}\cdot\frac{30c^3}{7b^2}=\frac{21\cdot 30}{10\cdot 7}\cdot b^{8-2}\cdot c^{3-6}=9b^6\cdot\frac{1}{c^3}$$

$$\frac{21b^8}{10c^6}:\frac{7b^2}{30c^3}=\frac{9b^6}{c^3}$$

2) $$\frac{40a^5b^9}{39c^6d^{14}}:\left(-\frac{5a^8b^3}{26c^{12}d^7}\right)=\frac{40a^5b^9}{39c^6d^{14}}\cdot\frac{26c^{12}d^7}{-5a^8b^3}$$

$$=-\frac{40\cdot 26}{39\cdot 5}\cdot a^{5-8}\cdot b^{9-3}\cdot c^{12-6}\cdot d^{7-14}=-\frac{16b^6c^6}{3a^3d^7}$$

3) $$36x^{16}y^{14}:\frac{18x^{18}y^{10}}{11m^3}=36x^{16}y^{14}\cdot\frac{11m^3}{18x^{18}y^{10}}$$

$$=2\cdot 11\cdot m^3\cdot x^{16-18}\cdot y^{14-10}=\frac{22m^3y^4}{x^2}$$

4) $$\frac{60m^6n^5}{17p^4}:(15m^8n^{10})=\frac{60m^6n^5}{17p^4}\cdot\frac{1}{15m^8n^{10}}$$

$$=\frac{60}{17\cdot 15}\cdot \frac{1}{m^2n^5p^4}=\frac{4}{17p^4m^2n^5}$$

5) $$\frac{17a^6b^{10}}{16c^2d^5}:\frac{34a^4b^4}{24c^6d^6}:\frac{15b^8d^4}{8a^8c^3}$$

$$=\frac{17a^6b^{10}}{16c^2d^5}\cdot\frac{24c^6d^6}{34a^4b^4}\cdot\frac{8a^8c^3}{15b^8d^4}$$

$$=\frac{17\cdot 24\cdot 8}{16\cdot 34\cdot 15}\cdot a^{6-4+8}\cdot b^{10-4-8}\cdot c^{-2+6+3}\cdot d^{-5+6-4}$$

$$=\frac{2a^{10}c^7}{5b^2d^3}$$

6) $$\left(-\frac{9x^5y^2}{7z^4}\right)^3:\left(-\frac{9x^4y^{10}}{7z^3}\right)^4$$

$$=-\frac{9^3x^{15}y^6}{7^3z^{12}}:\frac{9^4x^{16}y^{40}}{7^4z^{12}}=-\frac{9^3x^{15}y^6}{7^3z^{12}}\cdot\frac{7^4z^{12}}{9^4x^{16}y^{40}}$$

$$=-\frac{7}{9xy^{34}}$$

Ответ

1) $$\frac{9b^6}{c^3}$$; 2) $$-\frac{16b^6c^6}{3a^3d^7}$$; 3) $$\frac{22m^3y^4}{x^2}$$; 4) $$\frac{4}{17p^4m^2n^5}$$; 5) $$\frac{2a^{10}c^7}{5b^2d^3}$$; 6) $$-\frac{7}{9xy^{34}}$$.