To simplify the expression \((12^{53}) / (7^{53})\) using the Quotient Rule of Integer Exponents, we can apply the rule that states:
\[ \frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m \]
In this case, \(a\) is 12, \(b\) is 7, and \(m\) is 53.
So we can rewrite the expression as:
\[ \frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53} \]
This means the simplified form of \((12^{53}) / (7^{53})\) is \(\left(\frac{12}{7}\right)^{53}\).
Now, looking at the answer options provided:
- A) \(12^{106}\)
- B) \(\frac{12^{53}}{7^{53}}\)
- C) \(5^{106}\)
- D) \(5^{53}\)
The correct answer that matches our simplification is B: \(\frac{12^{53}}{7^{53}}\).
Thus, the final answer is B.