To simplify the expression \((12 \times 12 \times 12) \times (12 \times 12 \times 12)\) using the power rule of exponents, we first recognize that \(12 \times 12 \times 12\) can be expressed as \(12^3\).
Thus, we can rewrite the expression as:
\[ (12^3) \times (12^3) \]
According to the power rule of exponents, when we multiply two expressions with the same base, we add their exponents:
\[ 12^3 \times 12^3 = 12^{3+3} = 12^6 \]
Therefore, the simplified equivalent expression is:
\[ 12^6 \]
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