Hello, xXxSANJIxXx!

I found two different methods for these problems . . .

What are the last 2 digits of ?

Since 3^2)^{997} \:=\:9^{997} \:=\10 - 1)^{997}" alt="3^{1994} \:=\3^2)^{997} \:=\:9^{997} \:=\10 - 1)^{997}" />, consider the binomial expansion:

. .

. . . .

. . . . . . . . . These do not affect the last two digits

Therefore, the last two digits are: .

What are the last 2 digits of ?

We note that:

. . Hence: will end in .

Since , we have: .

. . . . .

. . (a number ending in )

Therefore, the last two digits of are: