TITLE: What is $2^{(k+1)} +2^{(k+1)}$ equal to?
QUESTION [5 upvotes]: I am so confused with this question. When the powers add we get $2^{2k+2}$ but in my book it says $2^{k+2}$. 
How is that? Please explain.

REPLY [12 votes]: You can't add the powers like that: $2^a+2^b$ is not the same as $2^{a+b}$.
What is true is that $2^a\cdot 2^b = 2^{a+b}$.
For your particular problem, we have $2^{k+1}+2^{k+1} = 2\cdot 2^{k+1} = 2^1\cdot 2^{k+1} = 2^{1+(k+1)} = 2^{k+2}$.

REPLY [5 votes]: $2^{k+1}+ 2^{k+1}=2 \cdot 2^{k+1}= 2^{k+2}$