Known: | x1-1 | + | x2-2 | + | x3-3 | +. + | x2002-2002 | + | x2003-2003 | = 0 find: 2 ^ X-2 ^ x2-2 ^ X3 -. - 2 ^ x2002 + 2 ^ x2003 Known: | x1-1 | + | x2-2 | + | x3-3 | +. + | x2002-2002 | + | x2003-2003 | = 0 Find the value of: 2 ^ X-2 ^ x2-2 ^ X3 -. - 2 ^ x2002 + 2 ^ x2003. (Note: similar to x2003, the following 2003 should be the subscript of x)

Known: | x1-1 | + | x2-2 | + | x3-3 | +. + | x2002-2002 | + | x2003-2003 | = 0 find: 2 ^ X-2 ^ x2-2 ^ X3 -. - 2 ^ x2002 + 2 ^ x2003 Known: | x1-1 | + | x2-2 | + | x3-3 | +. + | x2002-2002 | + | x2003-2003 | = 0 Find the value of: 2 ^ X-2 ^ x2-2 ^ X3 -. - 2 ^ x2002 + 2 ^ x2003. (Note: similar to x2003, the following 2003 should be the subscript of x)

|X1-1|+|X2-2|+|X3-3|+.+|X2002-2002|+|X2003-2003|=0
Sum of nonnegative numbers = 0
All items = 0
So X1 = 1, X2 = 2,... X2003 = x2003
therefore
2^X1-2^X2-2^X3-.-2^X2002+2^X2003
=2-2^2-2^3-2^4-...-2^2002+2^2003
=2-2^2-2^3-2^4-...-2^2001+(2^2003-2^2002)
=2-2^2-2^3-2^4-...-2^2001+(2*2^2002-2^2002)
=2-2^2-2^3-2^4-...-2^2001+2^2002
=All the way down, the last one down, but still + number
=2+2^2
=2+4=6