1. **State the problem:** Solve the equation $$0 = \left(\frac{1}{2}\right)^x$$ for $x$. 2. **Recall the properties of exponential functions:** For any base $a > 0$ and $a \neq 1$, the exponential function $a^x$ is always positive for all real $x$. That means $$\left(\frac{1}{2}\right)^x > 0 \quad \text{for all real } x.$$ 3. **Analyze the equation:** Since $$\left(\frac{1}{2}\right)^x$$ is always positive, it can never equal zero. 4. **Conclusion:** There is no real value of $x$ such that $$\left(\frac{1}{2}\right)^x = 0.$$ Therefore, the equation has **no solution**.