9^2004 = (10 - 1)^2004
So....the binomial expansion is
10^2004 - C(2004, 1) * 10^2003 + C(2004, 2)*10^2002 - ..... - C(2004,2002)(10)^2 + C(2004, 2003) (10) - 1
All of the terms except the last three end in "000"...so they add nothing to the sum of the last two digits in the expansion
And the last three terms are
-200,700,600 + 20040 - 1 =
abs [ -600 + 40 - 1 ]
abs [ -601 + 40 ] =
abs [-561 ] =
561
And the sum of the tens and the units digits in the expansion = 7