Упр.5.32 ГДЗ Мордкович 8 класс (Алгебра)

б) (-2a8b3/c7):(-4a10b4/c9)4;
в) (-2a2/b3)8*(b2/-2a3)2;
г) (-9x7y6/a12)4 *(-a8/27x5y4)3.

1. $$\left(\frac{x^2}{2a^3}\right)^3\cdot\left(\frac{4a^4}{x^3}\right)^2$$

   $$\frac{x^6}{8a^9}\cdot\frac{16a^8}{x^6}=\frac{16}{8}\cdot\frac{a^8}{a^9}=\frac{2}{a}$$

2. $$\left(\frac{-2a^8b^3}{c^7}\right)^5:\left(\frac{-4a^{10}b^4}{c^9}\right)^4$$

   $$\frac{-32a^{40}b^{15}}{c^{35}}:\frac{256a^{40}b^{16}}{c^{36}}=\frac{-32a^{40}b^{15}}{c^{35}}\cdot\frac{c^{36}}{256a^{40}b^{16}}=-\frac{c}{8b}$$

3. $$\left(\frac{-2a^2}{b^3}\right)^8\cdot\left(\frac{b^2}{-2a^3}\right)^2$$

   $$\frac{256a^{16}}{b^{24}}\cdot\frac{b^4}{4a^6}=\frac{64a^{10}}{b^{20}}$$

4. $$\left(\frac{-9x^7y^6}{a^{12}}\right)^4\cdot\left(\frac{-a^8}{27x^5y^4}\right)^3$$

   $$\frac{9^4x^{28}y^{24}}{a^{48}}\cdot\frac{-a^{24}}{27^3x^{15}y^{12}}=-\frac{3^8x^{13}y^{12}}{a^{24}\cdot3^9}=-\frac{x^{13}y^{12}}{3a^{24}}$$

Ответ

а) $$\frac{2}{a}$$; б) $$-\frac{c}{8b}$$; в) $$\frac{64a^{10}}{b^{20}}$$; г) $$-\frac{x^{13}y^{12}}{3a^{24}}$$.