Решебник по алгебре 8 класс Мерзляк ФГОС Задание 239

 

\[\boxed{\text{239\ (239).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ 1 = 3^{0},\ 3 = 3^{1},\ 9 = 3^{2},\ \]

\[27 = 3^{3},\ 81 = 3^{4},\ \]

\[\frac{1}{3} = 3^{- 1},\frac{1}{9} = 3^{- 2},\frac{1}{27} = 3^{- 3},\]

\[\frac{1}{81} = 3^{- 4}\]

\[2)\ 1 = \left( \frac{1}{3} \right)^{0},\ 3 = \left( \frac{1}{3} \right)^{- 1},\ \]

\[9 = \left( \frac{1}{3} \right)^{- 2},\ 27 = \left( \frac{1}{3} \right)^{- 3},\ \]

\[81 = \left( \frac{1}{3} \right)^{- 4},\]

\[\frac{1}{3} = \left( \frac{1}{3} \right)^{1},\frac{1}{9} = \left( \frac{1}{3} \right)^{2},\frac{1}{27} =\]

\[= \left( \frac{1}{3} \right)^{3},\frac{1}{81} = \left( \frac{1}{3} \right)^{4}\]

\[\boxed{\text{239.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ 5^{- 2} = \frac{1}{5^{2}} = \frac{1}{25}\]

\[2){\ 2}^{- 4} = \frac{1}{2^{4}} = \frac{1}{16}\]

\[3)\ ( - 9)^{- 2} = \frac{1}{( - 9)^{2}} = \frac{1}{81}\]

\[4)\ {0,2}^{- 3} = \frac{1}{{0,2}^{3}} = \frac{1}{0,008} =\]

\[= \frac{1000}{8} = 125\]

\[5)\ 1^{- 24} = \frac{1}{1^{24}} = 1\]

\[6)\ ( - 1)^{- 16} = \frac{1}{( - 1)^{16}} = 1\]

\[7)\ ( - 1)^{- 17} = \frac{1}{( - 1)^{17}} = - 1\]

\[8)\ \left( \frac{7}{8} \right)^{0} = 1\]

\[9)\ \left( \frac{2}{3} \right)^{- 3} = \frac{3^{3}}{2^{3}} = \frac{27}{8} = 3\frac{3}{8}\]

\[10)\ \left( - 1\frac{1}{6} \right)^{- 2} = \left( - \frac{7}{6} \right)^{- 2} =\]

\[= \frac{6^{2}}{7^{2}} = \frac{36}{49}\]