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

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

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

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Does the "." represent multiplication? –  Edison Apr 29 '12 at 5:04
$(2k)\cdot 2^{k+1}=k(2\cdot 2^{k+1})=k(2^{(k+1)+1})=k\cdot 2^{k+2}$. –  Brian M. Scott Apr 29 '12 at 5:05
@BrianM.Scott: that's it!! I was thinking how the k goes out. It is the associative law!! Thank you all. –  MIH1406 Apr 29 '12 at 5:09

1 Answer

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

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