To use the Product Rule of Exponents, you add the exponents when multiplying numbers with the same base.
The Product Rule states: \( a^m \cdot a^n = a^{m+n} \)
Let's evaluate the given options to see which one simplifies to \( 2412 \).
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\( 24^4 \cdot 24^8 \)
Using the Product Rule:
\( 24^4 \cdot 24^8 = 24^{4 + 8} = 24^{12} \) -
\( 24^3 \cdot 24^4 \)
Using the Product Rule:
\( 24^3 \cdot 24^4 = 24^{3 + 4} = 24^7 \) -
\( 12^4 \cdot 12^8 \)
Using the Product Rule:
\( 12^4 \cdot 12^8 = 12^{4 + 8} = 12^{12} \) -
\( 6^4 \cdot 4^3 \)
This expression has different bases, so the Product Rule doesn't directly apply; additional simplification would be needed.
None of the options simplify to \( 24^{12} \) directly, but since none of the options lead to 2412 (assuming it meant \( 24^{12} \)), if \( 2412 \) only refers to an exponent on 12, you'd still need to identify that no expression leads there either.
Looking again at the context:
If \( 2412 \) were meant as \( 24^{12} \), then the correct choice based on Product Rule is \( 24^4 \cdot 24^8 \).
That would be your answer: \( 24^4 \cdot 24^8\) simplifies correctly by the Product Rule to \( 24^{12} \), which appears to form the context claimed by number 2412 (as exponent-related).
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