To simplify the expression \( 12^{53} \div 7^{53} \) 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, let \( a = 12 \), \( b = 7 \), and \( m = 53 \). Applying the rule, we get:
\[ \frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53} \]
This means that the expression simplifies to \( \left(\frac{12}{7}\right)^{53} \).
From the options provided, the expression does not match any simplification as \( 12^{53} \div 7^{53} \) fully simplifies to \( \left(\frac{12}{7}\right)^{53} \). Therefore, the correct answer is:
None of the given options accurately represent the simplified form of the expression.
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