To simplify \((19^4)^9\), we can use the exponentiation rule \((a^m)^n = a^{m \cdot n}\).
Applying this rule here:
\[ (19^4)^9 = 19^{4 \cdot 9} \]
Calculating \(4 \cdot 9\):
\[ 4 \cdot 9 = 36 \]
So we have:
\[ (19^4)^9 = 19^{36} \]
Therefore, the simplified equivalent expression is \(19^{36}\).