1. **State the problem:** Solve the equation $$(0.25)^x = 16$$ for $x$. 2. **Recall the formula and rules:** We use the property of exponents that if $$a^x = a^y$$, then $$x = y$$, provided $$a > 0$$ and $$a \neq 1$$. 3. **Rewrite the bases as powers of the same number:** Note that $$0.25 = \frac{1}{4} = 4^{-1}$$ and $$16 = 4^2$$. 4. **Substitute these into the equation:** $$ (4^{-1})^x = 4^2 $$ 5. **Simplify the left side using the power of a power rule:** $$ 4^{-x} = 4^2 $$ 6. **Since the bases are equal, set the exponents equal:** $$ -x = 2 $$ 7. **Solve for $$x$$:** $$ x = -2 $$ **Final answer:** $$x = -2$$