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I've been playing with sage a bit and have been running into a number of walls in terms of getting analytical solutions so I decided to check if my beliefs are true about SAGE's difficulty with trying to solve the following algebraic problem in sage. $$x^a-c=0, c\geq0$$ on paper if we were to solve for this problem on paper we get $$x^*=c^{\frac{1}{a}}$$

What is simply done on paper seems to be an issue to run in sage:

x,a,c = var('x a c')
solve(x^a - c== 0)

This code does not work and wont give me the simple pen and paper solution to this problem. why is this the case?