1. **Problem Statement:** Find the power of a quotient, i.e., simplify the expression $$\left(\frac{a}{b}\right)^n$$ where $a$, $b$ are numbers and $n$ is an integer. 2. **Formula:** The power of a quotient rule states: $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$ This means you raise both the numerator and denominator to the power $n$ separately. 3. **Important Rules:** - $b \neq 0$ because division by zero is undefined. - If $n$ is positive, simply raise numerator and denominator to $n$. - If $n$ is negative, use the reciprocal: $$\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n = \frac{b^n}{a^n}$$ 4. **Example:** Simplify $$\left(\frac{2}{3}\right)^4$$ 5. **Step-by-step:** - Apply the rule: $$\left(\frac{2}{3}\right)^4 = \frac{2^4}{3^4}$$ - Calculate powers: $$2^4 = 16, \quad 3^4 = 81$$ - Final answer: $$\frac{16}{81}$$ 6. **Explanation:** Raising a quotient to a power means raising numerator and denominator separately to that power, which simplifies calculations and helps in algebraic manipulations. **Final answer:** $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$ and for the example, $$\left(\frac{2}{3}\right)^4 = \frac{16}{81}$$