To simplify the expression \( \frac{12 \cdot 5^{3}}{7 \cdot 5^{3}} \) using the Quotient Rule of Integer Exponents, we can follow these steps:
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Apply the Quotient Rule: When dividing like bases, subtract the exponents. Here, we have \( 5^3 \) in both the numerator and the denominator, so they cancel each other out:
\[ \frac{12 \cdot 5^{3}}{7 \cdot 5^{3}} = \frac{12}{7} \]
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The remaining expression does not have anything to combine or simplify further regarding exponents.
The simplified expression is:
\[ \frac{12}{7} \]
However, this does not match any of the options you provided. If you are looking for an alternative expression, the \( 5^{3} \) in the expression can actually be factored out, leading to the expression:
\[ \frac{12}{7} \cdot 5^{3} = 12(5^{3}) \div 7(5^{3}) = \frac{12}{7} \cdot 5^{3} \]
No option directly matches this result, so it appears there might be a small misalignment in what's expected from your choices. Would you like to choose from the options listed, or would you like further clarification?