1. ## 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.

2. 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.

$2^{x+1} + 2^{x-1} = 160$
$2^x 2^1 + 2^x 2^{-1} = 160$
$2^x \left( 2 + \frac{1}{2} \right) = 160$
$2^x \left( \frac{5}{2} \right) = 160$