(36^(324) * 33^(512) * 39 ^(180)) - (54^(29) * 25^(123) *31^(512))=(6∗1∗1)−(4∗5∗1)=(6∗1∗1)−(4∗5∗1)=6−0=6=6−0=6Steps:Find each of the unit number this way:Unit digit of36(324)36(324)Unit digit of:361=6,362=6,363=6....361=6,362=6,363=6....You can see the pattern here - Whatever the power is, the unit digit is 6.

Unit digit of33(512)33(512)Unit digit of:331=3,332=9,333=7,334=1,335=3...331=3,332=9,333=7,334=1,335=3...The pattern :3,9,7,13,9,7,1repeats after 4 blocks. Hence,mod(512/4)=0mod(512/4)=0Anything power 0 leaves 1 as unit digit.

Unit digit of39(180)39(180)Unit digit of:391=9,392=1,393=9....391=9,392=1,393=9....The pattern :9,19,1repeats after 2 blocks. Hence,mod(180/2)=0mod(180/2)=0Anything power 0 leaves 1 as unit digit.

Similarly,54(29)54(29)541=4,542=6,543=4...541=4,542=6,543=4...The pattern4,64,6repeats after 2 blocks. Somod(29/2)=1mod(29/2)=1Therefore, the corresponding unit digit is 4.

25(123)25(123)has a pattern of5,05,0repeating after 2 blocks. So,mod(123/2)=1mod(123/2)=1which corresponds to an unit digit of 5.

31(512)31(512)31 raised to power of anything yields an unit digit of 1. So, 1 is taken.

Hence, the answer is 6.