ГДЗ по алгебре 7 класс Макарычев Задание 546

\[\boxed{\text{546\ (546).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ p^{5} = x^{20}\]

\[\left( x^{y} \right)^{5} = x^{20}\]

\[x^{y \cdot 5} = x^{20}\]

\[y \cdot 5 = 20\]

\[y = 20\ :5 = 4.\]

\[Следовательно:\ \ p = x^{4}.\]

\[\textbf{б)}\ p^{7} = x^{21}\]

\[\left( x^{y} \right)^{7} = x^{21}\text{\ \ }\]

\[x^{y \cdot 7} = x^{21}\]

\[y \cdot 7 = 21\]

\[y = 21\ :7 = 3.\]

\[Следовательно:\ \ \ p = x^{3}.\]

\[\textbf{в)}\ p^{3} \cdot c^{8} = c^{20}\]

\[\left( c^{x} \right)^{3} \cdot c^{8} = c^{20}\text{\ \ }\]

\[x \cdot 3 + 8 = 20\]

\[3x = 20 - 8\]

\[3x = 12\]

\[x = 12\ :3 = 4.\]

\[Следовательно:\ \ p = c^{4}.\]

\[\textbf{г)}\ y^{7} \cdot \left( y^{2} \right)^{4} = p^{5}\]

\[y^{7} \cdot \left( y^{2} \right)^{4} = \left( y^{x} \right)^{5}\text{\ \ }\]

\[y^{7} \cdot y^{8} = y^{5 \cdot x}\]

\[7 + 8 = 5x\]

\[5x = 15\]

\[x = 15\ :5 = 3\]

\[Следовательно:\ \ \ p = y^{3}\text{.\ }\]