Inverse Z-transform mystic simplification
This is probably homework, so I'll just give you a few hints to get you on the right track. First of all, given an expression $X(z)$, the corresponding sequence is usually not unique. Your solution is correct if the region of convergence (ROC) of $X(z)$ is $|z|&gt;4$, which gives you an exponentially increasing sequence. If this were the impulse response of a discrete-time system, then the system would be causal but unstable.

The other solution assumes that the ROC is $\frac14&lt;|z|&lt;4$, which includes the unit circle. This corresponds to a two-sided decaying sequence. As an impulse response it would correspond to a non-causal but stable system.

So, to answer your question, both solutions are correct but they are not identical, because they are inverse transforms of $X(z)$ assuming different regions of convergence.