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The quick and dirty code for this is:

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

The quick and dirty code for this is:

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

The quick and dirty code for this is:

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

0,x)

The quick and dirty code for this is:

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