Simplify this expression using the Quotient Rule of Integer Exponents: 1253÷753.(1 point) Responses

Answer 1

To simplify the expression ${125}^3÷{75}^3$ using the Quotient Rule of Integer Exponents, we can first express it as:

$$\frac{{125}^3}{{75}^3}$$

According to the Quotient Rule, $\frac{a^m}{b^m}={\left(\frac{a}{b}\right)}^m$.

Using this rule, we get:

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

Now, we simplify $\frac{125}{75}$:

$$\frac{125}{75}=\frac{125÷25}{75÷25}=\frac{5}{3}$$

Now substitute this back into the expression:

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

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

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

So, the simplified form of the expression ${125}^3÷{75}^3$ is:

$$\frac{125}{27}$$