Упр.150 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (5m-2n)/10k : (5m-2n)/10k2;
2) (p+3)/(p2-2p) : (p+3)/(4p-8); Найдите частное:
1) 7/a2 : 28/a8;
2) b9/8 : b3/48;
3) 27/m6 : 36/m7n2;
4) 6×10/y8 : (30x5y2);
5) 49m4 : 21m/n2;
6) 16x3y8/33z5 : (-10×2/55z6).

1. $$\frac{5m-2n}{10k}:\frac{5m-2n}{10k^2}=\frac{5m-2n}{10k}\cdot\frac{10k^2}{5m-2n}=k.$$
2. $$\frac{p+3}{p^2-2p}:\frac{p+3}{4p-8}=\frac{p+3}{p(p-2)}\cdot\frac{4(p-2)}{p+3}=\frac{4}{p}.$$
3. $$\frac{7}{a^2}:\frac{28}{a^8}=\frac{7}{a^2}\cdot\frac{a^8}{28}=\frac{a^6}{4}.$$
4. $$\frac{b^9}{8}:\frac{b^3}{48}=\frac{b^9}{8}\cdot\frac{48}{b^3}=6b^6.$$
5. $$\frac{27}{m^6}:\frac{36}{m^7n^2}=\frac{27}{m^6}\cdot\frac{m^7n^2}{36}=\frac{3mn^2}{4}.$$
6. $$\frac{6x^{10}}{y^8}:(30x^5y^2)=\frac{6x^{10}}{y^8}\cdot\frac{1}{30x^5y^2}=\frac{x^5}{5y^{10}}.$$
7. $$49m^4:\frac{21m}{n^2}=49m^4\cdot\frac{n^2}{21m}=\frac{7m^3n^2}{3}.$$
8. $$\frac{16x^3y^8}{33z^5}:\left(-\frac{10x^2}{55z^6}\right)=\frac{16x^3y^8}{33z^5}\cdot\frac{55z^6}{-10x^2}=-\frac{8xy^8z}{3}.$$

Ответ

1) $$k$$; 2) $$\frac{4}{p}$$; 3) $$\frac{a^6}{4}$$; 4) $$6b^6$$; 5) $$\frac{3mn^2}{4}$$; 6) $$\frac{x^5}{5y^{10}}$$; 7) $$\frac{7m^3n^2}{3}$$; 8) $$-\frac{8xy^8z}{3}$$.