She is the author of the book Certificates of Positivity for Real Polynomials—Theory, Practice, and Applications (Springer, 2021).[2] A review on MathSciNet said that "In the reviewer's opinion this is a very nice and concise presentation of the most important pillars of real algebra up to the present time"
Powers' work moved from abstract real algebraic geometry to more concrete questions related to positive polynomials in one and several variables and voting theory. Her collaborators have included Eberhard Becker, Mari Castle, Bruce Reznick, Claus Scheiderer and Thorsten Wormann.
1991 "Holomorphy rings and higher level orders on skew fields", J. Algebra, vol. 136, no.1, 51-59.
1996 (with Eberhard Becker) "Sums of powers in rings and the real holomorphy ring", J. Reine Angew. Math., vol 480, 71-103.
1996 "Hilbert's 17th problem and the champagne problem", Amer. Math. Monthly, vol. 103, no.10, 879-887.
1998 (with Thorsten Wormann) "An algorithm for sums of squaresofreal polynomials", J. Pure Appl. Algebra, vol. 127, no.1, 99-104.
2000 (with Bruce Reznick) "Polynomials that are positive on an interval", Trans. Amer. Math. Soc., vol. 352, no. 10, 4677-4692.
2000 (with Bruce Reznick) "Notes towards a constructive proof of Hilbert's theorem on ternary quartics", Quadratic forms and their applications (Dublin 1999), Contemp. Math. vol. 272, 209-227.
2001 (with Claus Scheiderer) "The moment problem for non-compact semialgebraic sets.", Adv. Geom, vol.1, 71-88
2001 (with Bruce Reznick) "A new bound for Polya's theorem with applications to polynomials positive on polyhedra", J. Pure Appl. Algebra, vol.164, no. 1-2, 221-229.
2004 (with Bruce Reznick, Claus Scheiderer, and Frank Sottile) "A new approach to Hilbert's theorem on ternary quartics", C. R. Acad. Sci. Paris, vol. 339, no.9, 617-620.