**Problem:** Solve the exponential equation $$10^x = \frac{1}{10,000}$$. 1. Recognize that 10,000 can be written as a power of 10: $$10,000 = 10^4$$. 2. Rewrite the equation using this notation: $$10^x = \frac{1}{10^4}$$. 3. Recall that $$\frac{1}{10^4} = 10^{-4}$$. So the equation becomes $$10^x = 10^{-4}$$. 4. Since the bases are the same and both sides are equal, the exponents must be equal: $$x = -4$$. **Final answer:** $$x = -4$$.