To simplify the expression \( 125^3 \div 75^3 \) using the Quotient Rule of Integer Exponents, we can use the property:
\[ \frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m \]
In this case, we have:
\[ \frac{125^3}{75^3} = \left(\frac{125}{75}\right)^3 \]
Next, we can simplify \( \frac{125}{75} \):
\[ \frac{125}{75} = \frac{125 \div 25}{75 \div 25} = \frac{5}{3} \]
Now substituting back, we have:
\[ \left(\frac{125}{75}\right)^3 = \left(\frac{5}{3}\right)^3 = \frac{5^3}{3^3} = \frac{125}{27} \]
Therefore, the simplified form of \( 125^3 \div 75^3 \) is \( \frac{125}{27} \).
However, none of the provided responses match this derived expression. If you meant something equivalent in an exponent form or a different expression, please clarify for further analysis.
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