To apply the Product Rule of Exponents, we use the rule that states \( a^m \cdot a^n = a^{m+n} \).
Given the expression \( 24^{12} \), we need to find how it can be written in a form that exemplifies the Product Rule.
Let's analyze the options provided:
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\( 12^4 \times 12^8 \): This simplifies to \( 12^{(4 + 8)} = 12^{12} \), which is not \( 24^{12} \).
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\( 6^4 \times 4^3 \): This does not simplify to \( 24^{12} \) since \( 6 \) and \( 4 \) are not the same base.
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\( 24^4 \times 24^8 \): This simplifies to \( 24^{(4 + 8)} = 24^{12} \). This is the correct expression to show \( 24^{12} \).
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\( 24^3 \times 24^4 \): This simplifies to \( 24^{(3 + 4)} = 24^{7} \), which is not \( 24^{12} \).
Thus, the expression that correctly uses the Product Rule of Exponents to simplify to \( 24^{12} \) is:
\( 24^4 \times 24^8 \).