1. **State the problem:** Solve the equation $$\frac{3^x}{81} = -27$$. 2. **Recall the properties:** The base 3 raised to any real power is always positive, so $$3^x > 0$$ for all real $$x$$. 3. **Analyze the equation:** The left side $$\frac{3^x}{81}$$ is positive because both numerator and denominator are positive. 4. **Right side:** The right side is $$-27$$, which is negative. 5. **Conclusion:** Since a positive number cannot equal a negative number, there is **no solution** to this equation. **Final answer:** No solution exists because $$\frac{3^x}{81}$$ cannot be negative.