1. **State the problem:** Simplify the expression $2^{k+1} + 2^{k+1}$. 2. **Recall the rule for adding like terms with exponents:** When terms have the same base and exponent, you can factor them out. 3. **Factor the expression:** $$2^{k+1} + 2^{k+1} = 2 \times 2^{k+1}$$ 4. **Use the property of exponents:** $$2 \times 2^{k+1} = 2^{1} \times 2^{k+1} = 2^{1 + (k+1)} = 2^{k+2}$$ 5. **Final answer:** $$2^{k+1} + 2^{k+1} = 2^{k+2}$$ This means adding two identical powers of two results in doubling the value, which increases the exponent by 1.