To simplify the expression \(\left(a^{3}\right)^{4}\), we apply the power of a power property of exponents, which states that \((x^m)^n = x^{m \cdot n}\).
Here, we have:
\[ \left(a^{3}\right)^{4} = a^{3 \cdot 4} = a^{12} \]
Thus, the simplified expression is:
\[ \boxed{a^{12}} \]
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