To simplify \((5^8)^4\) using the Power Rule of Exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
In this case:
\[ (5^8)^4 = 5^{8 \cdot 4} \]
So, the equivalent form of \((5^8)^4\) is:
\[ 5^{(8 \cdot 4)} \]
Therefore, the correct response is:
5 superscript left parenthesis 8 times 4 right parenthesis baseline.