# 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 $x > N_c$,
$$|g(x)|<{\frac {1}{x^{c}}}.$$
If you mean a constant $n$, then $g(x)=(f(x))^n=(1/2)^n$ is non-negligible.
• Just judging from the information you provided, If $n$ is a constant, then yes it is non-negligible. However, double check your proof because in proofs $n$ is often a security parameter that is not a constant. – Changyu Dong Jun 7 '18 at 15:29