Exponent problem!!

**Revelsyn** · September 6th 2007, 05:38 PM

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**topsquark** · September 6th 2007, 06:05 PM

Originally Posted by Revelsyn

I got a review of exponents sheet last math class and I can't figure out how to do this one ><; I've been given the answer but I don't understand the process; help anyone

"Evaluate."

2–n(2n - 2¹+ n)

~ everything in red is an exponent
~the sheet says the answer is supposed to be -1

$2^{-n} \left ( 2^n - 2^{1 + n} \right )$

First, note that multiplication is distributive over addition, so this is:
$2^{-n} \left ( 2^n - 2^{1 + n} \right ) = 2^{-n} \cdot 2^n - 2^{-n} \cdot 2^{1 + n}$

Now use the property that
$a^x \cdot a^y = a^{x + y}$

So:
$= 2^{-n + n} - 2^{-n + 1 + n} = 2^0 - 2^1$

$= 1 - 2 = -1$

-Dan

**Krizalid** · September 6th 2007, 06:08 PM

Other way

$2^{-n}(2^n-2^{1+n})=2^{-n}\cdot2^n(1-2)=-1$

Cheers,
K.

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