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This paper studies the uniqueness of meromorphic functions f^n\prod_{i=1}^k(f^{(i)})^{n_i}\quadand\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).