Question

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

5106
5 superscript 106 baseline

553
5 superscript 53 baseline

12106
12 superscript 106 baseline

1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline

Answer 1

To simplify the expression \( \frac{12^{53}}{7^{53}} \) using the Quotient Rule of Integer Exponents, you can express it as:

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

The options listed don't explicitly include this form, so let’s interpret each option:

1. **5106** - This doesn't represent the expression.
2. **553** - This incorrectly suggests \(5^{53}\).
3. **12106** - This incorrectly suggests \(12^{106}\), which is not relevant here.
4. **1253÷753** - This represents \( \frac{12^{53}}{7^{53}} \).

The most direct answer from the options would be:

**1253÷753.**

Hence, the simplified expression is \( \frac{12^{53}}{7^{53}} \) or \( \left(\frac{12}{7}\right)^{53} \).