implify. 1) \( \frac{\left(36 x^{2}\right)^{\frac{1}{2}}}{3 x^{-1}} \) (2) \( \frac{\left(64 x^{-6}\right)^{\ddagger}}{2 x^{3}} \) (3) \( \frac{(025 \mathrm{~m})^{\frac{1}{4}}}{25 .\left(\mathrm{m}^{-1}\right)^{2}} \) (4) \( \frac{\left(49 x^{2}\right)^{\frac{1}{2}}}{\left(7^{3}\right)^{\frac{1}{2}} \cdot x^{-\frac{1}{2}}} \) (5) \( \frac{\left(9 x^{3}\right)^{\frac{1}{2}} \cdot\left(x^{\frac{1}{2}}\right)^{-1}}{\left(3 x^{2}\right)^{2}} \) (6) \( \frac{\left(x^{3}\right)^{\frac{-}{4}} \cdot\left(x^{\frac{1}{3}}\right)^{2}}{\left(x^{\frac{1}{6}}\right)^{2}} \)

Let’s simplify these expressions step by step! 1) \[ \frac{\left(36 x^{2}\right)^{\frac{1}{2}}}{3 x^{-1}} = \frac{6 x}{3 x^{-1}} = \frac{6 x \cdot x}{3} = \frac{6 x^{2}}{3} = 2 x^{2} \] 2) \[ \frac{\left(64 x^{-6}\right)^{\ddagger}}{2 x^{3}} = \frac{(8 x^{-3})^{2}}{2 x^{3}} = \frac{64 x^{-6}}{2 x^{3}} = \frac{64}{2} x^{-6-3} = 32 x^{-9} \] 3) \[ \frac{(25 \mathrm{~m})^{\frac{1}{4}}}{25 .\left(\mathrm{m}^{-1}\right)^{2}} = \frac{(25)^{\frac{1}{4}} \cdot m^{\frac{1}{4}}}{25 \cdot m^{-2}} = \frac{5^{\frac{1}{2}} m^{\frac{1}{4}}}{25 m^{-2}} = \frac{5^{\frac{1}{2}} m^{\frac{1}{4}} m^{2}}{25} = \frac{5^{\frac{1}{2}} m^{\frac{9}{4}}}{25} \] 4) \[ \frac{\left(49 x^{2}\right)^{\frac{1}{2}}}{\left(7^{3}\right)^{\frac{1}{2}} \cdot x^{-\frac{1}{2}}} = \frac{7 x}{7^{\frac{3}{2}} \cdot x^{-\frac{1}{2}}} = \frac{7 x \cdot x^{\frac{1}{2}}}{7^{\frac{3}{2}}} = \frac{7 x^{\frac{3}{2}}}{7^{\frac{3}{2}}} = \frac{x^{\frac{3}{2}}}{7^{1}} = \frac{x^{\frac{3}{2}}}{\sqrt{7^{3}}} \] 5) \[ \frac{\left(9 x^{3}\right)^{\frac{1}{2}} \cdot\left(x^{\frac{1}{2}}\right)^{-1}}{\left(3 x^{2}\right)^{2}} = \frac{3 x^{\frac{3}{2}} \cdot x^{-\frac{1}{2}}}{9 x^{4}} = \frac{3 x^{1}}{9 x^{4}} = \frac{x}{3 x^{4}} = \frac{1}{3 x^{3}} \] 6) \[ \frac{\left(x^{3}\right)^{-\frac{1}{4}} \cdot\left(x^{\frac{1}{3}}\right)^{2}}{\left(x^{\frac{1}{6}}\right)^{2}} = \frac{x^{-\frac{3}{4}} \cdot x^{\frac{2}{3}}}{x^{\frac{1}{3}}} = \frac{x^{-\frac{3}{4} + \frac{2}{3}}}{x^{\frac{1}{3}}} = x^{-\frac{3}{4} + \frac{8}{12} - \frac{4}{12}} = x^{-\frac{3}{4} + \frac{4}{12}} = x^{-0.5} \] If you need any further clarification or detailed steps for any of the problems, feel free to ask!