Question

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

Answer 1

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 $8$ .