Let \(n\) be a prime with \(n\equiv 1\pmod 4\). Let \(\zeta\) be a primitive \(n\)th root of unity, \(K=\mathbb{Q}(\zeta)\) and \({\mathcal O}_ K\) the ring of integers of \(K\). For any two elements \(\alpha\) and \(\beta\) of \({\mathcal O}_ K\), which are prime to \(n\) and to each other, \((\alpha/\beta)_ n\) denotes the \(n\)th power residue symbol over \(K\). let \(p\) and \(q\) be two prime numbers \(\equiv 1\pmod n\). Suppose \(p=N_{K/\mathbb{Q}}(\pi)\) and \(q=N_{K/\mathbb{Q}}(\omega)\), where \(\pi,\omega\in {\mathcal O}_ K\). An explicit expression for \((p/\omega)_ n(q/\pi)_ n^{-1}\) is obtained. It is shown in the case \(n=5\) that this expression involves only power residue characters of rational integers and Jacobi sums.