unfortunately it's not that simple. (a+b)^2=a^2+2ab+b^2, and not a^2+b^2. (a+b)^3=a^3+3a^2b+3ab^2+b^3, and not a^3+b^3. It only gets more and more complicated, but Pascal's triangle gives you the coefficients (the number BEFORE the letters (the number 2 in 2ab, for instance)). If you don't know what that is, Google "Pascal's Triangle".
The exponents are easy to find when n is a number, but I don't know how to expand it when it's just n. When it's a number all you do is to gradually move the exponents over from one part to the other (from a to b in (a+b)^n), one by one. For instance, (a+b)^5 has 6 parts when expanded. The first is a^5. Pretty easy. The second is a^4b, or a^(5-1)b^1. Third is a^3b^2, or a^(5-2)b^2. You get the point. Add in the coefficients from Pascal's triangle and you get (a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5. You certainly don't get a^5+b^5.
The exponents are easy to find when n is a number, but I don't know how to expand it when it's just n. When it's a number all you do is to gradually move the exponents over from one part to the other (from a to b in (a+b)^n), one by one. For instance, (a+b)^5 has 6 parts when expanded. The first is a^5. Pretty easy. The second is a^4b, or a^(5-1)b^1. Third is a^3b^2, or a^(5-2)b^2. You get the point. Add in the coefficients from Pascal's triangle and you get (a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5. You certainly don't get a^5+b^5.