# Indicies Problem

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• Jan 2nd 2009, 02:46 AM
StaryNight
Indicies Problem
I am asked to show that: 2^(x+1) + 2^(x-1) = 160 can be written as 2.5 * (2^x) =160

Could somebody please show me the steps taken to do this simplification? Since there is an addition, I can't get the rules of indicies to help me. In other questions like this I have always been able to use substitution/factorisation but i can't see a common factor.

Thanks for your help.
• Jan 2nd 2009, 02:52 AM
janvdl
Quote:

Originally Posted by StaryNight
I am asked to show that: 2^(x+1) + 2^(x-1) = 160 can be written as 2.5 * (2^x) =160

Could somebody please show me the steps taken to do this simplification? Since there is an addition, I can't get the rules of indicies to help me. In other questions like this I have always been able to use substitution/factorisation but i can't see a common factor.

Thanks for your help.

$\displaystyle 2^{x+1} + 2^{x-1} = 160$

$\displaystyle 2^x 2^1 + 2^x 2^{-1} = 160$

$\displaystyle 2^x \left( 2 + \frac{1}{2} \right) = 160$

$\displaystyle 2^x \left( \frac{5}{2} \right) = 160$