Question

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

Answer 1

To simplify the expression \( 125^3 \div 75^3 \) using the Quotient Rule of Integer Exponents, we can use the property of exponents that states:

\[
\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m
\]

So we can rewrite the expression as:

\[
\frac{125^3}{75^3} = \left(\frac{125}{75}\right)^3
\]

Next, we simplify \( \frac{125}{75} \):

\[
\frac{125}{75} = \frac{125 \div 25}{75 \div 25} = \frac{5}{3}
\]

Now we substitute back into the expression:

\[
\left(\frac{125}{75}\right)^3 = \left(\frac{5}{3}\right)^3
\]

Now we can calculate \( \left(\frac{5}{3}\right)^3 \):

\[
\left(\frac{5}{3}\right)^3 = \frac{5^3}{3^3} = \frac{125}{27}
\]

Thus, the simplified expression \( 125^3 \div 75^3 \) is:

\[
\frac{125}{27}
\]

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