Contour plot within upper and lower bounds

Question

I have a mathematical function $f(p,q)=10^{-10}\frac{p^4}{q^2}$. I want to make a contour plot within the region where $10^{-3}<f(p,q)<10^{+3}$. I have tried the following three codes (one is similar to this one), but their outputs are different. Could you suggest me a better way to draw the contour plot of that function?

ContourPlot[{If[
   10^-3 < (10^-10* (x^4)/y^2) < 10^3, (10^-10* (x^4)/y^2)]}, {x, 
  10^-3, 10^3}, {y, -1, 1}, FrameLabel -> {"p", "q"}, 
 ContourLabels -> True, PlotLegends -> Automatic]

ContourPlot[{ConditionalExpression[(10^-10* (x^4)/y^2), 
   10^-3 < (10^-10* (x^4)/y^2) < 10^3]}, {x, 10^-3, 10^3}, {y, -1, 1},
  FrameLabel -> {"p", "q"}, ContourLabels -> True, 
 PlotLegends -> Automatic]

RegionPlot[{10^-3 < (10^-10* (x^4)/y^2) < 10^3}, {x, 10^-3, 
  10^3}, {y, -1, 1}, FrameLabel -> {"p", "q"}, 
 PlotLegends -> Automatic]

Answer 1

Something happens near y==0...

As a workaround try

 Show[{ContourPlot[(10^-10*(x^4)/y^2), {x, 10^-3, 1000}, {y, 10^-3, 1},
    PlotPoints -> 100 , 
   RegionFunction -> 
    Function[{x, y, z}, 10^-3 < (10^-10*(x^4)/y^2) < 10^3]],
  ContourPlot[(10^-10*(x^4)/y^2), {x, 10^-3, 1000}, {y, -1, -10^-3 }, 
   PlotPoints -> 100 , 
   RegionFunction -> 
    Function[{x, y, z}, 10^-3 < (10^-10*(x^4)/y^2) < 10^3]]}, 
 PlotRange -> All]

Hope it helps!