The expression that is correctly developed to use the Power Rule of Exponents is:
\[(7^{4})^{8}\]
According to the Power Rule, \((a^{m})^{n} = a^{m \cdot n}\). This rule can be applied to this expression, but the others do not involve a situation where the Power Rule is applicable (especially the first and last options).
Thus, the best answer is \((7^{4})^{8}\).