What is $2^{(k+1)} +2^{(k+1)}$ equal to?

Question

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.

Answer 1

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 $2^{k+1}+2^{k+1} = 2\cdot 2^{k+1} = 2^1\cdot 2^{k+1} = 2^{1+(k+1)} = 2^{k+2}$.

Answer 2

$2^{k+1}+ 2^{k+1}=2 \cdot 2^{k+1}= 2^{k+2}$