To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the quotient rule of integer exponents, we can rewrite it as follows:
\[ \frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53} \]
Now, substituting back, we have:
\[ \left(\frac{12}{7}\right)^{53} \]
Thus, the simplified expression is \( \left(\frac{12}{7}\right)^{53} \).
Among the given options, this matches with \( \frac{12^{53}}{7^{53}} \), meaning the most accurate representation of this simplified expression in the provided options is:
12^53 divided by 7^53.
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