To simplify the expression \((12 \cdot 12 \cdot 12) \cdot (12 \cdot 12 \cdot 12)\) using the Power Rule of Exponents, we first recognize that we can express each group of \(12\)s as an exponent.
The expression \(12 \cdot 12 \cdot 12\) can be rewritten as \(12^3\) (since there are three \(12\)s multiplied together). Therefore, the original expression becomes:
\[ (12^3) \cdot (12^3) \]
Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\), we combine the two \(12^3\) terms:
\[ 12^3 \cdot 12^3 = 12^{3+3} = 12^6 \]
Thus, the simplified equivalent expression is:
\[ \boxed{12^6} \]
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