1. **State the problem:** Simplify the expression $$2^{-4} + 2^{-2}$$. 2. **Recall the rule for negative exponents:** $$a^{-n} = \frac{1}{a^n}$$ where $a \neq 0$ and $n$ is a positive integer. 3. **Rewrite each term using positive exponents:** $$2^{-4} = \frac{1}{2^4} = \frac{1}{16}$$ $$2^{-2} = \frac{1}{2^2} = \frac{1}{4}$$ 4. **Add the fractions:** $$\frac{1}{16} + \frac{1}{4}$$ 5. **Find a common denominator:** The least common denominator of 16 and 4 is 16. 6. **Rewrite the second fraction with denominator 16:** $$\frac{1}{4} = \frac{\cancel{1} \times 4}{\cancel{4} \times 4} = \frac{4}{16}$$ 7. **Add the fractions:** $$\frac{1}{16} + \frac{4}{16} = \frac{1+4}{16} = \frac{5}{16}$$ 8. **Final answer:** $$2^{-4} + 2^{-2} = \frac{5}{16}$$