If a, b are opposite numbers to each other and a is not equal to 0, find 2009 of power +(a/b) of 2008 of a+b/a-b+(b/a)

If a, b are opposite numbers to each other and a is not equal to 0, find 2009 of power +(a/b) of 2008 of a+b/a-b+(b/a)

A, b are mutually opposite numbers
A+b=0 a=-b
2008 Power of a+b/a-b+(b/a)+(a/b)2009
=0+(-1)^2008+(-1)^2009
=1-1
=0

If a, b are mutually opposite numbers, c, d are mutually reciprocal, and a is not equal to 0, then the value of (a+b)2009 power +(cd)2010 power -(a/b)2011 power If a, b are mutually opposite numbers, c, d are reciprocal, and a is not equal to 0, then the value of (a+b)2009 power +(cd)2010 power -(a/b)2011 power

If a, b are reciprocal, c, d are reciprocal,
Then: a+b=0; cd=1
A/b =-1

2009 Power of (a+b)+2010 power of (cd)-2011 power of (a/b)
=0+1-(-1)
=1+1
=2