On the generalization of two results of Cao and Zhang

summary:This paper studies the uniqueness of meromorphic functions $$f^{n}\prod _{i=1}^{k}(f^{(i)})^{n_{i}}\quad \mbox {and}\quad g^{n}\prod _{i=1}^{k}(g^{(i)})^{n_{i}}$$ that share two values, where $n, n_{k}, k\in \mathbb {N}$, $n_{i}\in \mathbb {N}\cup \{0\}$, $i=1,2,\ldots ,k-1$. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012)