Упр.152 ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (a6/b3)10;
2) (-4m/9n3)2;
3) (-10c7/3d5)3;
4) (2m3n2/kp8)6. Выполните деление:
1) (5m-2n)/10k : (5m-2n)/10k2;
2) (p+3)/(p2-2p) : (p+3)/(4p-8);

1. $$\left(\frac{a^6}{b^3}\right)^{10}=\frac{(a^6)^{10}}{(b^3)^{10}}=\frac{a^{60}}{b^{30}}.$$

2. $$\left(\frac{-4m}{9n^3}\right)^2=\frac{(-4m)^2}{(9n^3)^2}=\frac{16m^2}{81n^6}.$$

3. $$\left(\frac{-10c^7}{3d^5}\right)^3=\frac{(-10c^7)^3}{(3d^5)^3}=-\frac{1000c^{21}}{27d^{15}}.$$

4. $$\left(\frac{2m^3n^2}{kp^8}\right)^6=\frac{(2m^3n^2)^6}{(kp^8)^6}=\frac{64m^{18}n^{12}}{k^6p^{48}}.$$

5. $$\frac{5m-2n}{10k}:\frac{5m-2n}{10k^2}=\frac{5m-2n}{10k}\cdot\frac{10k^2}{5m-2n}=k.$$

6. $$\frac{p+3}{p^2-2p}:\frac{p+3}{4p-8}=\frac{p+3}{p(p-2)}\cdot\frac{4(p-2)}{p+3}=\frac{4}{p}.$$

Ответ

1) $$\frac{a^{60}}{b^{30}}$$; 2) $$\frac{16m^2}{81n^6}$$; 3) $$-\frac{1000c^{21}}{27d^{15}}$$; 4) $$\frac{64m^{18}n^{12}}{k^6p^{48}}$$; 5) $$k$$; 6) $$\frac{4}{p}$$.