To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the Quotient Rule of Integer Exponents, we can apply the rule which states that \( \frac{a^m}{b^m} = \left( \frac{a}{b} \right)^m \).
So, we have:
\[ \frac{12^{53}}{7^{53}} = \left( \frac{12}{7} \right)^{53} \]
Among the given responses:
- \( 12^{106} \)
- \( 5^{106} \)
- \( \frac{12^{53}}{7^{53}} \)
- \( 5^{53} \)
The expression \( \frac{12^{53}}{7^{53}} \) is already presented as one of the options, so the simplified form can remain as \( \frac{12^{53}}{7^{53}}\).
Thus, the correct response is:
\( \frac{12^{53}}{7^{53}} \).