Question

Temple this expression using the quotation rule of integer exponents: 12⁵³÷7⁵³

5⁵³
12¹⁰⁶
12⁵³÷7⁵³
5¹⁰⁶

Answer 1

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the rule of integer exponents, we can rewrite it as follows:

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

Since this is a direct application of the quotient rule of exponents, we see that it simplifies to:

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

Thus, among the options provided, the closest equivalent expression that captures the essence of the original expression is:

\[
12^{53} \div 7^{53} \quad \text{or} \quad \frac{12^{53}}{7^{53}}
\]

However, none of the options seem to exactly match this result.

If we purely follow the options you provided without making further assumptions or derivations, the expression \( 12^{53} \div 7^{53} \) would be the proper step resulting from "templating" the original expression.

Since none of the listed options seem directly valid, if you're looking for a transformation that fits \( \frac{12^{53}}{7^{53}} \), then \( 12^{53} \div 7^{53} \) is indeed the correct interpretation, while another approach would yield simpler, yet not exact equivalent forms.

If a decision must be made directly on provided options, you may want to pick \( 12^{53} \div 7^{53} \) for correctness or organization before further manipulation.