How to reach $k\cdot 2^{k+2}$ from $(2k)\cdot 2^{k+1}$?

Question

I was trying to figure out the step between these two equal expression:

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

$(2k)\cdot 2^{k+1}=k(2\cdot 2^{k+1})=k(2^{(k+1)+1})=k\cdot 2^{k+2}$.
@BrianM.Scott: that's it!! I was thinking how the k goes out. It is the associative law!! Thank you all.

Edison · Accepted Answer · 2012-04-29 05:31:57Z

up vote 1 down vote accepted

HINT A number raised to an exponent tells you how many times to multiply that number by itself.

For example: $2^{k}=2*2*...*2$ k-times, so $2*2^{k}=2*(2*2*...*2)$ a total of $k+1$ times so $2*2^{k}=2^{k+1}$

edited Apr 29 '12 at 5:31

answered Apr 29 '12 at 5:07

Edison
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