Question

The last digit of the number $3^{400}$

• A. $3$
• B. $9$
• C. $7$
• D. $1$

Answer 1

The correct option is D $1$

$3^{400}$
$=(3^4{)}^{100}$
$=(1+80{)}^{100}$
$=1+{}^{100}{C}_1\left(80\right)+...{}^{100}{C}_n(80{)}^{100}$
$=1+80\left(k\right)$ where $k$ is positive integer.
Hence the last digit is one