Решебник по алгебре 8 класс Макарычев ФГОС Задание 1183

\(\boxed{\text{1183.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\)

\[x^{n} = ?;\ \ x^{- n} = ?\]

\[\textbf{а)}\ x = \frac{1}{2};\ \ n = 2:\]

\[x^{n} = \left( \frac{1}{2} \right)^{2} = \frac{1}{4};\]

\[x^{- n} = \left( \frac{1}{2} \right)^{- 2} = 2^{2} = 4.\]

\[\textbf{б)}\ x = - \frac{1}{3};\ \ n = 3:\]

\[x^{n} = \left( - \frac{1}{3} \right)^{3} = - \frac{1}{27};\]

\[x^{- n} = \left( - \frac{1}{3} \right)^{- 3} = ( - 3)^{3} = - 27.\]

\[\textbf{в)}\ x = \frac{2}{3};\ \ n = - 2:\]

\[x^{n} = \left( \frac{2}{3} \right)^{- 2} = \left( \frac{3}{2} \right)^{2} = \frac{9}{4};\]

\[x^{- n} = \left( \frac{2}{3} \right)^{- ( - 2)} = \left( \frac{2}{3} \right)^{2} = \frac{4}{9}.\]

\[\textbf{г)}\ x = - 1,5;\ \ n = 3:\]

\[x^{n} = ( - 1,5)^{3} = \left( - \frac{3}{2} \right)^{3} = - \frac{27}{8};\]

\[x^{- n} = ( - 1,5)^{- 3} = \left( - \frac{3}{2} \right)^{- 3} =\]

\[= \left( - \frac{2}{3} \right)^{3} = - \frac{8}{27}.\]