Powers in a ring

Question

Ler $R$ be a ring with unity $1_R$. If $x \in R $ and $n \in \mathbb{Z} $ how can I compute $(-x)^n $?. Is it equal to $-x^n $ or $x^n $?

Answer 1

$(-x)^n = ((-1) \cdot x)^n = (-1)^nx^n$. Whether this is $-x^n$ or $x^n$ will depend whether $n$ is odd or even.