Questions: Use the power rule and the power of a product or quotient rule to simplify the expression. [ left(fracrsright)^4 ] (left(fracrsright)^4=) (Use positive exponents only.)

$Use the power rule and the power of a product or quotient rule to simplify the expression. [ left(fracrsright)^4 ] (left(fracrsright)^4=) (Use positive exponents only.)$

Transcript text: Use the power rule and the power of a product or quotient rule to simplify the expression. \[ \left(\frac{r}{s}\right)^{4} \] $\left(\frac{r}{s}\right)^{4}=$ $\square$ (Use positive exponents only.)

Solution

Solution Steps

To simplify the expression $\left(\frac{r}{s}\right)^{4}$, we can use the power of a quotient rule. This rule states that $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. Applying this rule will allow us to express the given expression with positive exponents.

Step 1: Apply the Power of a Quotient Rule

To simplify the expression $\left(\frac{r}{s}\right)^{4}$, we apply the power of a quotient rule, which states that $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$. Thus, we can rewrite the expression as: \[ \left(\frac{r}{s}\right)^{4} = \frac{r^{4}}{s^{4}} \]

Step 2: Final Expression

The simplified expression is now in the form of a fraction with positive exponents: \[ \frac{r^{4}}{s^{4}} \]