# How to find regular values for $g(x,y,z)=x^a y^b z^c - N$

I'm solving a problem of Lagrange multipliers for $$f(x,y,z)=Ax+By+Cz$$ subject to $$x^a y^b z^c=N$$ where $$a,b,c,A,B,C,N$$ are constants

I need to find a smooth manifold in order to use the Lagrange theorem, and for doing this I should find a regular value for $$g(x,y,z)=x^a y^b z^c - N$$. Which may be a regular value for $$g$$ or how can I find it?