<< Graphics`ImplicitPlot`

kolo = 
      ImplicitPlot[
        x^2 + y^2 == 16^(2/5), {x, -3, 3}, {y, -3, 
          3}]

eq1 = x^5 == 16

sol = Solve[eq1, x]

x1 = x /.  sol[[1]]
x2 = x /.  sol[[2]]
x3 = x /.  sol[[3]]
x4 = x /.  sol[[4]]
x5 = x /.  sol[[5]]

l1 = {{Re[x1], Im[x1]}, {Re[x2], Im[x2]}}  // 
        N
l2 = {{Re[x2], Im[x2]}, {Re[x3], Im[x3]}}  // 
        N
l3 = {{Re[x3], Im[x3]}, {Re[x4], Im[x4]}}  // 
        N
l4 = {{Re[x4], Im[x4]}, {Re[x5], Im[x5]}}  // 
        N
l5 = {{Re[x5], Im[x5]}, {Re[x1], Im[x1]}}  // N

lista  = Sort[ Union[l1, l2, l3, l4, l5] ]

punkty  =  
      ListPlot[lista, PlotStyle -> PointSize[0.02]]

g1 = Graphics[{Line[l1]}]
g2 = Graphics[{Line[l2]}]
g3 = Graphics[Line[l3]]
g4 = Graphics[Line[l4]]
g5 = Graphics[Line[l5]]

Show[kolo, punkty, g1, g2, g3, g4, g5, 
      PlotRange -> {{-3, 3}, {-3, 3}}]