Question

The last three digits of the number $(27{)}^{27}$ is

• A. 805
• B. 301
• C. 503
• D. 803

Answer 1

Answer: (D)

$(27{)}^{27}=3^{81}=3\cdot (9{)}^{40}$
$=3(10-1{)}^{40}=3\left(10^{40}-{}^{40}{C}_1\cdot 10^{39}+\dots ..+{}^{40}{C}_{38}\cdot 10^2-{}^{40}{C}_{39}\cdot 10+1\right)$
$=3(1000\lambda -400+1)$
Last 3 digits of this number $=803$.