1. The problem is to understand how to add expressions with the same base in algebra. 2. When you have terms with the same base raised to the same exponent, such as $a^n + a^n$, you can add them by combining the coefficients: $a^n + a^n = 2a^n$. 3. However, if the exponents are different, for example $a^m + a^n$ where $m \neq n$, you cannot add them directly because they are not like terms. 4. In summary, addition works like this: - If bases and exponents are the same: $a^n + a^n = 2a^n$ - If bases are the same but exponents differ: $a^m + a^n$ cannot be simplified further. 5. This is because addition combines like terms, and like terms must have the same variable part (same base and exponent). 6. For multiplication or division with the same base, different rules apply, but for addition, only like terms can be combined. Final answer: Add coefficients only when the bases and exponents are the same.