Question

Simplify this expression using the Quotient Rule of Integer Exponents: 1253÷753 .(1 point) Responses 553 5 superscript 53 baseline 5106 5 superscript 106 baseline 12106 12 superscript 106 baseline 1253÷753 12 superscript 53 baseline divided by 7 superscript 53 baseline

Answer 1

To simplify the expression \( \frac{125^3}{75^3} \) using the Quotient Rule of Integer Exponents, we can rewrite it as follows:

1. First, identify the base and apply the Quotient Rule:
\[
\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m
\]
So, we can rewrite:
\[
\frac{125^3}{75^3} = \left(\frac{125}{75}\right)^3
\]

2. Now, simplify the fraction:
\[
\frac{125}{75} = \frac{125 \div 25}{75 \div 25} = \frac{5}{3}
\]

3. So we get:
\[
\left(\frac{5}{3}\right)^3 = \frac{5^3}{3^3} = \frac{125}{27}
\]

Hence, the simplified expression for \( \frac{125^3}{75^3} \) is \( \frac{125}{27} \).

From the options provided:
- 553
- \( 5^{53} \)
- \( 5^{106} \)
- \( 12^{106} \)
- \( 12^{53} \) divided by \( 7^{53} \)

It looks like none of these match our simplified expression of \( \frac{125}{27} \). Please verify if there's any additional context or constraints that might change the evaluation.