1. **State the problem:** Simplify the expression $$\left(\frac{v}{9}\right)^2$$. 2. **Formula used:** When squaring a fraction, use the rule $$\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$$. 3. **Apply the formula:** Here, $$a = v$$ and $$b = 9$$, so $$\left(\frac{v}{9}\right)^2 = \frac{v^2}{9^2}$$. 4. **Simplify the denominator:** Since $$9^2 = 81$$, the expression becomes $$\frac{v^2}{81}$$. 5. **Final answer:** The simplified form of $$\left(\frac{v}{9}\right)^2$$ is $$\frac{v^2}{81}$$. This means you square both numerator and denominator separately.