What is the last digit of the 2010 power of 3 plus (-2)

What is the last digit of the 2010 power of 3 plus (-2)

=3^2010+2^2010
3 At the end is 3
3^2 End 9
3^3 End7
3^4 End1
3,9,7,1 Cycles
2010÷4 Has no remainder, so the end is 1
2 End2
2^2 End4
2^3 End 8
2^4 End6
2,4,8,6 Cycles
2010÷4 Has no remainder, so the end is 6
So at the end of 3^2010+2^2010 is 6+1=7

(2000 Power of 2000+2001 power of 2001) divided by 2001 power of 2000+2002 power of 2001 {(2000 Power of 2000+2001 power of 2001)/(2001 power of 2000+2002 power of 2001)}*10 Steps to find the integer part of this result ·····

Let 2000^2000= a,2001^2001= b
N/10=(2000a+2000b+b)/(a+b)
=2000+B/(a+b)
Because 1> b/(a+b)> b/(2001^2000+b)=0.9995
So n/10=2000.9.
Integer part n =20009.