1. **State the problem:** Solve the equation $$(0.25)^x = 16$$ using indices. 2. **Rewrite the bases as powers of the same number:** Note that $0.25 = \frac{1}{4} = 4^{-1}$ and $16 = 4^2$. 3. **Substitute these into the equation:** $$ (4^{-1})^x = 4^2 $$ 4. **Use the power of a power rule:** $$ 4^{-x} = 4^2 $$ 5. **Since the bases are the same, set the exponents equal:** $$ -x = 2 $$ 6. **Solve for $x$:** $$ x = -2 $$ **Final answer:** $$ x = -2 $$