To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the Quotient Rule of Integer Exponents, we can apply the rule that states \( \frac{a^m}{b^m} = \left( \frac{a}{b} \right)^m \).
So, we have:
\[ \frac{12^{53}}{7^{53}} = \left( \frac{12}{7} \right)^{53} \]
Therefore, the expression simplifies to \( \left( \frac{12}{7} \right)^{53} \).
Among the given options, we can express this simplification directly or see which matches our result. The closest simplification that matches this is \( 12^{53} ÷ 7^{53} = \frac{12^{53}}{7^{53}} \), but since none of the choices fits this exact formulation, we evaluate them:
- \( 5^{106} \) (not related)
- \( 12^{106} \) (not related)
- \( 5^{53} \) (not related)
- \( 12^{53} ÷ 7^{53} \) (this is what we started with)
Since none of the choices directly correspond to our simplification \( \left( \frac{12}{7} \right)^{53} \), the best representation of our result in a simplified form is \( 12^{53} ÷ 7^{53} \).
Thus, the final answer is:
\( 12^{53} ÷ 7^{53} \).
1 answer