Use the power rule \[ \left(5 p^{7}\right)^{2} \]

To simplify the expression \(\left(5 p^{7}\right)^{2}\) using the power rule, we apply the rule that states \((a \cdot b)^{n} = a^{n} \cdot b^{n}\). Here, we can treat \(5\) and \(p^{7}\) as \(a\) and \(b\) respectively, with \(n\) as \(2\). So, we have: \[ \left(5 p^{7}\right)^{2} = 5^{2} \cdot \left(p^{7}\right)^{2} = 25 \cdot p^{14} \] Thus, the simplified expression is: \[ 25 p^{14} \]