simplify `(2^(2009)-2^(2007))/(2^(2006)-2^(2008))`

Simplify ((2011^(2)-2017)(2011^(2)+4022-3)(2012))/(2013.2014.2008.2010)

x^(2009) xx(1)/(x^(2008))=x

A set B contains 2007 elements. Let c be the set consisting of subsets of B which contain at most 1003 elements. The number of elements in C is (A) 2^(2005) (B) 2^(2006) (C) 2^(1003) (D) 2^(2007)

Let f(x)=((2007)^(x))/((2007)^(x)+sqrt(2007)) then the sum f((1)/(2007))+f((2)/(2007))+f((3)/(2007))+....f((2006)/(2007))

Let f(x)=(2007^(x))/(2007^(x)+sqrt(2007)) Then find the value of quad 2007^(x)+sqrt(2007)(1)/(2)+f((2)/(2008))+f((3)/(2008))+...+f((2007)/(2008))

sin ((pi) / (2 ^ (2009))) cos ((pi) / (2 ^ (2009))) cos ((pi) / (2 ^ (2008))) ...... cos ( (pi) / (2 ^ (2)))

For x!=0,+-1, the expression (((1)/(x^(2007))-(1)/(x^(2009)))/((1)/(x^(2008))-(1)/(x^(2010)))) is

The value of integral int_(0)^(2008)(3x^(2)-8028x+(2007)^(2)+(1)/(2008))dx equals (2008)^(2) b.(2009)^(2) c.2009d.1