- I recommend
Stanley Burris and Karen Yeats, The Saga of the High School Identities. Algebra Universalis, 52 nos.2-3 (2005), 325-342. https://people.math.sfu.ca/~kya17/papers/saga_paper4.pdf
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If you want some cosmic pessimism, try:
R. Gurevic, Equational theory of positive numbers with exponentiation is not finitely
axiomatizable. Annal of Pure and Applied Logic 49 (1990), 1–30. https://www.jstor.org/stable/2044966