1. ## Exponent problem!!

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

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

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

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

$\displaystyle = 1 - 2 = -1$

-Dan

3. Other way

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

Cheers,
K.