Answer
16
Work Step by Step
Based on the power of a quotient rule, we know that $\frac{a^{m}}{{a}^{n}}=a^{m-n}, a\ne0$ (where $m$ and $n$ are positive integers and $a$ is a real number).
Therefore, $\frac{(-2)^{14}}{(-2)^{10}}=(-2)^{14-10}=(-2)^{4}=16$.