\[\boxed{\text{172\ (}\text{н}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\mathbf{Если\ }\mathbf{a > 0;\ \ n -}\mathbf{натуральное\ }\]
\[\mathbf{число,\ больше\ 1,\ то:}\]
\[\sqrt[\mathbf{n}]{\mathbf{a}}\mathbf{=}\mathbf{a}^{\frac{\mathbf{1}}{\mathbf{n}}}\mathbf{.}\]
Решение.
\[\textbf{а)}\ \left( \sqrt[4]{7} \right)^{4} = \left( 7^{\frac{1}{4}} \right)^{4} = 7;\]
\[\textbf{б)}\ \left( \sqrt[7]{- 3} \right)^{7} = \left( - 3^{\frac{1}{7}} \right)^{7} = - 3;\]
\[\textbf{в)}\ \left( 2\sqrt[4]{3} \right)^{4} = 2^{4} \cdot \left( 3^{\frac{1}{4}} \right)^{4} =\]
\[= 16 \cdot 3 = 48;\]
\[\textbf{г)}\ \left( - 3\sqrt[3]{2} \right)^{3} = - 3^{3} \cdot \left( 2^{\frac{1}{3}} \right)^{3} =\]
\[= - 27 \cdot 2 = - 54.\]
\[\textbf{д)}\ \left( - \sqrt[7]{- 28} \right)^{7} = - 28^{1} = - 28\ \ \]
\[\textbf{е)}\ \left( 3\sqrt[3]{8} \right)^{3} = 3^{3} \cdot 8^{1} = 27 \cdot 8 =\]
\[= 216\]
\[\boxed{\text{172\ (}\text{с}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\mathbf{Если\ }\mathbf{a > 0;\ \ n -}\mathbf{натуральное\ }\]
\[\mathbf{число,\ больше\ 1,\ то:}\]
\[\sqrt[\mathbf{n}]{\mathbf{a}}\mathbf{=}\mathbf{a}^{\frac{\mathbf{1}}{\mathbf{n}}}\mathbf{.}\]
Решение.
\[\textbf{а)}\ \left( \sqrt[4]{7} \right)^{4} = \left( 7^{\frac{1}{4}} \right)^{4} = 7;\]
\[\textbf{б)}\ \left( \sqrt[7]{- 3} \right)^{7} = \left( - 3^{\frac{1}{7}} \right)^{7} = - 3;\]
\[\textbf{в)}\ \left( 2\sqrt[4]{3} \right)^{4} = 2^{4} \cdot \left( 3^{\frac{1}{4}} \right)^{4} =\]
\[= 16 \cdot 3 = 48;\]
\[\textbf{г)}\ \left( - 3\sqrt[3]{2} \right)^{3} = - 3^{3} \cdot \left( 2^{\frac{1}{3}} \right)^{3} =\]
\[= - 27 \cdot 2 = - 54.\]
\[\boxed{\text{172.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[y = \frac{3x - 2}{x - 2}\]
\[\frac{3x - 2}{x - 2} = 0\]
\[3x - 2 = 0\]
\[3x = 2\]
\[x = \frac{2}{3}.\]
\[y > 0\ \ при\ \ \]
\[x \in \left( - \infty;\frac{2}{3} \right) \cup (2;\ + \infty);\]
\[y < 0\ \ при\ x \in \left( \frac{2}{3};2 \right).\]