Question

If $\left(2^{35}{3}^{16}\right)$ is divided by $11$ , then the remainder is:

Answer 1

Answer: 8

Consider $2^{35}{3}^{16}=2^3\left(4^{16}{3}^{16}\right)=8{\left(1+11\right)}^{16}=8\left(\_{}^{16}{C}_0^{}+\_{}^{16}{C}_1^{}11+\_{}^{16}{C}_2^{}{\left(11\right)}^2+...+{\left(11\right)}^{16}\right)$
$=8+11k$ , where $k$ (some integer)
Therefore, $2^{35}{3}^{16}$ when divided by $11$ leaves the remainder $8$ .