To simplify the expression \((12 \times 12 \times 12) \times (12 \times 12 \times 12)\) using the power rule of exponents, we can first rewrite each term in exponential form.
The term \(12 \times 12 \times 12\) can be expressed as \(12^3\). Therefore, the expression becomes:
\[ (12^3) \times (12^3) \]
According to the power rule of exponents, when multiplying like bases, you add the exponents:
\[ 12^3 \times 12^3 = 12^{3+3} = 12^6 \]
So the simplified equivalent expression is:
\[ \boxed{12^6} \]