-2 To the 2001 power plus -2 to the 2002 power How much is it? I count -2, - Power of -2 plus 2002 power of -2 How much is it? I count -2,

-2 To the 2001 power plus -2 to the 2002 power How much is it? I count -2, - Power of -2 plus 2002 power of -2 How much is it? I count -2,

(-2)^2001+(-2)^2002=(-2)^2001*(1+(-2))=-1*(-2)^2001
Because (-2)^2001 is a negative number, the 2^2001
2 To the 2001 power.

(-2)^2001+(-2)^2002=(-2)^2001*(1+(-2))=-1*(-2)^2001
Because (-2)^2001 is negative, the original formula =2^2001
2 To the 2001 power.

Given |x+y-3(the square of x-y-1=0, find the 2006th power of the algebraic equation x and the 2005th power of the (-y) Given |x+y-3||+(the square of x-y-1=0, find the 2006th power of the algebraic equation x and the 2005th power of the (-y)

The absolute value and the square are greater than or equal to 0, and the sum is equal to 0. If one is greater than 0, the other is less than 0.
So both equal 0.
So x+y-3=0
X-y-1=0
So x=2, y=1
Therefore, the original formula =1^2006*(-1)2005
=1*(-1)
=-1

The absolute value and the square are greater than or equal to 0, and the sum is equal to 0. If one is greater than 0, the other is less than 0.
So both equals zero.
So x+y-3=0
X-y-1=0
So x=2, y=1
Therefore, the original formula =1^2006*(-1)2005
=1*(-1)
=-1