To simplify the expression \((12 \cdot 12 \cdot 12) \cdot (12 \cdot 12 \cdot 12)\) using the power rule of exponents, we first can rewrite each group of three 12's:
\[ 12 \cdot 12 \cdot 12 = 12^3 \]
Thus, we can rewrite the entire expression as:
\[ (12^3) \cdot (12^3) \]
Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\), we combine the exponents:
\[ (12^3) \cdot (12^3) = 12^{3+3} = 12^6 \]
Therefore, the simplified equivalent expression is:
\[ 12^6 \]
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