ГДЗ по алгебре 8 класс Мерзляк Задание 257

\[\boxed{\text{257\ (257).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\text{\ a}^{- 2} + a^{- 3} = \frac{1^{\backslash a}}{a^{2}} + \frac{1}{a^{3}} =\]

\[= \frac{a + 1}{a^{3}}\]

\[2)\ mn^{- 4} + m^{- 4}n =\]

\[= \frac{m^{\backslash m^{4}}}{n^{4}} + \frac{n^{\backslash n^{4}}}{m^{4}} = \frac{m^{5} + n^{5}}{m^{4}n^{4}}\]

\[3)\ \left( c^{- 1} - d^{- 1} \right) \cdot (c - d)^{- 2} =\]

\[= \left( \frac{1^{\backslash d}}{c} - \frac{1^{\backslash c}}{d} \right) \cdot \frac{1}{(c - d)^{2}} =\]

\[= \frac{d - c}{\text{cd}} \cdot \frac{1}{(c - d)^{2}} =\]

\[= \frac{(d - c) \cdot 1}{\text{cd}(d - c)^{2}} = \frac{1}{\text{cd}(d - c)}\]

\[4)\ \left( x^{- 2} + y^{- 2} \right) \cdot \left( x^{2} + y^{2} \right)^{- 1} =\]

\[= \left( \frac{1^{\backslash y^{2}}}{x^{2}} + \frac{1^{\backslash x^{2}}}{y^{2}} \right) \cdot \ \frac{1}{x^{2} + y^{2}} =\]

\[= \frac{x^{2} + y^{2}}{x^{2}y^{2}} \cdot \frac{1}{x^{2} + y^{2}} =\]

\[= \frac{(x^{2} + y^{2})}{x^{2}y^{2}(x^{2} + y^{2})} = \frac{1}{x^{2}y^{2}}\]