Hence or otherwise calculte the value of 2 to the power 2010 plus 2 to the power 2012 plus 10 divide by 2 to the power 2009 plus 1

it appears you want

2^2010 + 2^2012 + 10
---------------------------
2^2009 + 1

(2^2009*2 + 2^2009*8 + 10)/(2^2009+1)

(2^2009*10 + 10)/(2^2009+1)

10(2^2009+1)/(2^2009+1)

10