Question

find the last digits and last three digits of the number (27)^27​

Answer 1

27^27= (3^3)^27 =3^81=

3*3^80=3*(3^2)^40

=3*9^40

=3*(10-1)^40 expanding (10-1)^40 (by binomial theoram)

=3*(10^40- 40C1*10^39+................+40C38*10^2- 40C39*10 +1)

EXCEPT 40C39*10 AND 1 EVERY EXPANSION IS MULTIPLE OF 1000 SO AS WE WANT THE LAST THREE DIGITS WE'LL CONSIDER THE REST TERMS AS 1000X {TAKING 1000 COMMON FROM ALL THE OTHER TERMS } X BE ANY INTEGER

=3*(1000X-400+1)

=3*(1000X-399)

3000X-1197

AS THE LAST THREE DIGITS OF 3000X WILL BE 000

....000-1197=....803

SO THE LAST THREE DIGITS ARE 803

Answer 2

Step-by-step explanation:

803... I think answer

correct