1. **State the problem:** Solve the equation $$\frac{1}{x^2} - 16 = 0$$ for $x$. 2. **Rewrite the equation:** Add 16 to both sides to isolate the fraction: $$\frac{1}{x^2} = 16$$ 3. **Use the reciprocal property:** Taking the reciprocal of both sides gives: $$x^2 = \frac{1}{16}$$ 4. **Solve for $x$:** Take the square root of both sides: $$x = \pm \sqrt{\frac{1}{16}} = \pm \frac{1}{4}$$ 5. **Final answer:** The solutions are $$x = \frac{1}{4} \quad \text{or} \quad x = -\frac{1}{4}$$