a) $\sqrt[6]125 = \sqrt[6]5^3 = \sqrt5$ b) $\sqrt[4]6561$ $6561 = 3^8$ $\left. \beginarrayc|c6561 & 3\cr2187 & 3 \cr729 & 3 \cr243 & 3 \cr81 & 3 \cr27 & 3 \cr9 & 3 \cr3 & 3 \cr1\endarray \right.$ $\sqrt[4]6561 = \sqrt[4]3^8 = \sqrt[4]3^4 \cdot 3^4 = 3 \cdot 3 = 9$ (…)