To simplify the expression \((78^8)^6\) using the Power Rule of Exponents, you multiply the exponents together. The Power Rule states that \((a^m)^n = a^{m \cdot n}\).
Applying this rule:
\[ (78^8)^6 = 78^{8 \cdot 6} = 78^{48} \]
So, the simplified expression is:
\[ 78^{48} \]