Question

Simplify this expression using the Quotient Rule of Integer Exponents: 12 to the power of 53÷7 to the power of 53
.(1 point)
Responses

5106
5 superscript 106 baseline

12106
12 superscript 106 baseline

553
5 superscript 53 baseline

1253÷753

Answer 1

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the Quotient Rule of Integer Exponents, we can apply the rule that states \( \frac{a^m}{b^m} = \left( \frac{a}{b} \right)^m \).

Applying this rule, we get:

\[
\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}
\]

Thus, the expression simplifies to:

\[
\left(\frac{12}{7}\right)^{53}
\]

None of the options perfectly match this result, but if we look further, one option is \( 12^{53} \div 7^{53} \), which is an alternate representation of the same solution.

If any specific numerical expression was aimed for in this context, or if additional context regarding the options is needed, please provide further clarification!