To simplify the expression \( 125^3 \div 75^3 \) using the Quotient Rule of Integer Exponents, we can first express it as:
\[ \frac{125^3}{75^3} \]
According to the Quotient Rule, \( \frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m \).
Using this rule, we get:
\[ \frac{125^3}{75^3} = \left(\frac{125}{75}\right)^3 \]
Now, we simplify \( \frac{125}{75} \):
\[ \frac{125}{75} = \frac{125 \div 25}{75 \div 25} = \frac{5}{3} \]
Now substitute this back into the expression:
\[ \left(\frac{125}{75}\right)^3 = \left(\frac{5}{3}\right)^3 \]
Now calculate \( \left(\frac{5}{3}\right)^3 \):
\[ \left(\frac{5}{3}\right)^3 = \frac{5^3}{3^3} = \frac{125}{27} \]
So, the simplified form of the expression \( 125^3 \div 75^3 \) is:
\[ \frac{125}{27} \]