Is power of non-negligible function non-negligible? If I have a probability which is > negl(n), i.e., non-negligible, will be this probability raised to the power of n also non-negligible?
No and yes, depending on what do you mean by $n$. 

Take $f(x)=1/2$ for example. It is a non-negligible function, but $g(x)=(f(x))^x=(1/2)^{x}$ is negligible, i.e. for every positive integer $c$, there exists an integer $N_c$ such that for all $x &gt; N_c$,

$$|g(x)|&lt;{\frac {1}{x^{c}}}.$$

If you mean a constant $n$, then $g(x)=(f(x))^n=(1/2)^n$ is non-negligible.