\[\boxed{\text{539\ (539).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Пусть\ \text{x\ }и\ y - искомые\ числа.\]
\[Составим\ систему\ уравнений:\]
\[\left\{ \begin{matrix} xy = 15 \cdot (x + y) \\ x + 2y = 100\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = 100 - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 100y - 2y^{2} = 15 \cdot (100 - y) \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x = 100 - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2y^{2} - 115y + 1500 = 0 \\ \end{matrix} \right.\ \]
\[D = 115^{2} - 4 \cdot 2 \cdot 1500 = 1225\]
\[y_{1,2} = \frac{115 \pm 35}{4} = 20;37,5;\]
\[\left\{ \begin{matrix} y_{1} = 20 \\ x_{1} = 60 \\ \end{matrix} \right.\ \ \ \ или\ \ \ \left\{ \begin{matrix} y_{2} = 37,5 \\ x_{2} = 25.\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:60\ и\ 20\ или\ \ 25\ и\ 37,5.\]
\[\boxed{\text{539.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ 81 \cdot 3^{- 6} = 3^{4} \cdot 3^{- 6} = 3^{- 2} = \frac{1}{9}.\]
\[\textbf{б)}\ \frac{\left( - 3^{- 3} \right)^{3}}{- 9^{- 2}} = \frac{3^{- 9}}{3^{- 4}} = 3^{- 5} = \frac{1}{243}.\]
\[\textbf{в)}\ 9^{- 5} \cdot \left( \frac{1}{9} \right)^{- 3} =\]
\[= 3^{- 10} \cdot \left( 3^{- 2} \right)^{- 3} = 3^{- 10} \cdot 3^{6} =\]
\[= 3^{- 4} = \frac{1}{81}.\]
\[\textbf{г)}\ \left( - 3^{- 3} \right)^{2} \cdot 27³ = 3^{- 6} \cdot 3^{9} = 27.\ \]