I posted this question on [cstheory](https://cstheory.stackexchange.com/questions/19443/what-does-textpoly-stand-for-in-o-log10-5n-cdot-textpoly-log-log) and found that "poly(f(n))" is shorthand for "polynomial in f(n)" or $f(n)^{O(1)}$, hence poly(log log n) is shorthand for $(log log n)^{O(1)}$. However, I don't understand the notation where the big oh is an exponent. I understand big oh notation but not when big oh itself is an exponent. Why have the word poly at all in the expression? Can anybody explain how this works or refer me to some articles?