how to solve the 5th root of 243 please show steps having pr

how to solve the 5th root of -243. please show steps. having problem solving for the nth roots.

Solution

243 = 3*81 = 3*3*27 = 3*3*3*9 = 3*3*3*3*3 = 3⁵ . Therefore -243 = -3⁵. Now, (-243)^1/5 = ( -3⁵)^1/5 = 3 (-1)^1/5 = -3 as (-1)^1/5 = -1. The answer is -3