Упр.55 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

$$\frac{17x^{-8}}{14y^{-12}}\cdot \frac{28y}{51x^{-21}}= \frac{17\cdot 28\cdot x^{-8}\cdot y\cdot y^{12}\cdot x^{21}}{14\cdot 51}$$

$$=\frac{17\cdot 2\cdot x^{13}y^{13}}{51}=\frac{2x^{13}y^{13}}{3}$$

$$-1{,}6m^{-4}n^3\cdot(-2m^{-3}p^{-6})^{-3}$$

$$=-\frac{16n^3}{10m^4}\cdot \frac{1}{(-2m^{-3}p^{-6})^3} =-\frac{16n^3}{10m^4}\cdot \frac{1}{-8m^{-9}p^{-18}}$$

$$=\frac{16n^3m^9p^{18}}{80m^4}=\frac{n^3m^5p^{18}}{5}=0{,}2n^3m^5p^{18}$$

$$2\frac14 a^{-5}b\cdot\left(1\frac12 a^{-1}b^{-3}\right)^{-3}$$

$$=\frac94 a^{-5}b\cdot\left(\frac32 a^{-1}b^{-3}\right)^{-3} =\frac94 a^{-5}b\cdot \left(\frac{2}{3a^{-1}b^{-3}}\right)^3$$

$$=\frac94 a^{-5}b\cdot \frac{8}{27a^{-3}b^{-9}} =\frac94\cdot \frac{8a^3b^9\cdot b}{27a^5}$$

$$=\frac{2b^{10}}{3a^2}$$

$$(-10a^{-2}bc^{-11})^{-2}\cdot(0{,}1bc^{-2})^{-3}$$

$$=\frac{1}{(-10a^{-2}bc^{-11})^2}\cdot \left(\frac{1}{10bc^{-2}}\right)^3$$

$$=\frac{1}{100a^{-4}b^2c^{-22}}\cdot \frac{1}{1000b^3c^{-6}} =\frac{10a^4c^{22}c^6}{b^5}$$

$$=\frac{10a^4c^{28}}{b^5}$$

$$\left(-\frac15 a^{-3}b^{-7}\right)^{-3}\cdot(-5a^2b^6)^{-2}$$

$$=\left(-\frac{5}{a^{-3}b^{-7}}\right)^3\cdot \left(\frac{1}{-5a^2b^6}\right)^2 =-\frac{125}{a^{-9}b^{-21}}\cdot \frac{1}{25a^4b^{12}}$$

$$=-\frac{125a^9b^{21}}{25a^4b^{12}}=-5a^5b^9$$

$$\left(\frac{8p^{-4}}{q^{-1}}\right)^{-2}\cdot(16p^{-6}q^3)^3$$

$$=\left(\frac{q^{-1}}{8p^{-4}}\right)^2\cdot(2^4p^{-6}q^3)^3 =\frac{q^{-2}}{(2^3)^2p^{-8}}\cdot 2^{12}p^{-18}q^9$$

$$=\frac{2^{12}q^7p^{-18}}{2^6q^2p^{-8}} =\frac{2^6q^7}{p^{10}}=\frac{64q^7}{p^{10}}$$