Does $2^{k+1} = 2^k * 2^1$?

Question

I'm not sure how to deal with an exponent like this. Can I simplify it into terms that are easier to work with?

I know that $2^3 · 2^4 = 2^{3+4} = 128$, but I don't know about $2^{k + 1}$

Answer 1

Yes, $2^{k+1} ≡ 2·2^{k}$

And that is roughly as simplified as $2^{k+1}$ can get.

Of course you can rewrite it in many different ways, but without the context of a problem it is hard to know which one is best.

For instance, you can rewrite it as $e^{x·\ln{2}}$.