Найдите значения выражения а) корень 4 степени под корнем 3*корень 3 степени под 9 все это разделить на корень 6 степени под корнем 9* на корень под корнем 3
Два способа: можно работать с корнями, а можно со степенями
![\frac{\sqrt[4]{3\sqrt[3]{9}}}{\sqrt[6]{9\sqrt{3}}} = \frac{\sqrt[4]{\sqrt[3]{3^{3} \cdot 3^{2}}}}{\sqrt[6]{\sqrt{3 \cdot 3^{4}}}} = \frac{\sqrt[7]{3^{5}}}{\sqrt[7]{3^{5}}} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B4%5D%7B3%5Csqrt%5B3%5D%7B9%7D%7D%7D%7B%5Csqrt%5B6%5D%7B9%5Csqrt%7B3%7D%7D%7D+%3D+%5Cfrac%7B%5Csqrt%5B4%5D%7B%5Csqrt%5B3%5D%7B3%5E%7B3%7D+%5Ccdot+3%5E%7B2%7D%7D%7D%7D%7B%5Csqrt%5B6%5D%7B%5Csqrt%7B3+%5Ccdot+3%5E%7B4%7D%7D%7D%7D+%3D+%5Cfrac%7B%5Csqrt%5B7%5D%7B3%5E%7B5%7D%7D%7D%7B%5Csqrt%5B7%5D%7B3%5E%7B5%7D%7D%7D+%3D+1 "\frac{\sqrt[4]{3\sqrt[3]{9}}}{\sqrt[6]{9\sqrt{3}}} = \frac{\sqrt[4]{\sqrt[3]{3^{3} \cdot 3^{2}}}}{\sqrt[6]{\sqrt{3 \cdot 3^{4}}}} = \frac{\sqrt[7]{3^{5}}}{\sqrt[7]{3^{5}}} = 1")
![\frac{\sqrt[4]{3\sqrt[3]{9}}}{\sqrt[6]{9\sqrt{3}}} = \frac{(3\cdot 3^{\frac{2}{3}})^{\frac{1}{4}}}{(3^{2} \cdot 3^{\frac{1}{2}})^\frac{1}{6}} = \frac{3^{\frac{5}{3}\cdot \frac{1}{4}}}{3^{\frac{5}{2}\cdot \frac{1}{6}}} = \frac{3^{\frac{5}{12}}}{3^{\frac{5}{12}}} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B4%5D%7B3%5Csqrt%5B3%5D%7B9%7D%7D%7D%7B%5Csqrt%5B6%5D%7B9%5Csqrt%7B3%7D%7D%7D+%3D+%5Cfrac%7B%283%5Ccdot+3%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%7B%283%5E%7B2%7D+%5Ccdot+3%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%5E%5Cfrac%7B1%7D%7B6%7D%7D+%3D+%5Cfrac%7B3%5E%7B%5Cfrac%7B5%7D%7B3%7D%5Ccdot+%5Cfrac%7B1%7D%7B4%7D%7D%7D%7B3%5E%7B%5Cfrac%7B5%7D%7B2%7D%5Ccdot+%5Cfrac%7B1%7D%7B6%7D%7D%7D+%3D+%5Cfrac%7B3%5E%7B%5Cfrac%7B5%7D%7B12%7D%7D%7D%7B3%5E%7B%5Cfrac%7B5%7D%7B12%7D%7D%7D+%3D+1 "\frac{\sqrt[4]{3\sqrt[3]{9}}}{\sqrt[6]{9\sqrt{3}}} = \frac{(3\cdot 3^{\frac{2}{3}})^{\frac{1}{4}}}{(3^{2} \cdot 3^{\frac{1}{2}})^\frac{1}{6}} = \frac{3^{\frac{5}{3}\cdot \frac{1}{4}}}{3^{\frac{5}{2}\cdot \frac{1}{6}}} = \frac{3^{\frac{5}{12}}}{3^{\frac{5}{12}}} = 1")