To simplify the expression \((78 \cdot 8)^6\) using the Power Rule of Exponents, we apply the rule which states that \((a \cdot b)^n = a^n \cdot b^n\).
So, we can rewrite the expression as follows:
\[ (78 \cdot 8)^6 = 78^6 \cdot 8^6 \]
This is the simplified form of the expression. If you need numerical values, you can calculate \(78^6\) and \(8^6\) separately, but the expression in its simplified algebraic form is:
\[ 78^6 \cdot 8^6 \]