Explanation

(c)
Now, $7^{9} = (8 - 1)^{9} = - 1(1 - 8)^{9}$
$= - 1 + \ ^{9}C_{1}8 - \ ^{9}C_{2}8^{2} + ... + \ ^{9}C_{9}8^{9}$ and $9^{7} = {(1 + 8)}^{7}$
$= 1 + \ ^{7}C_{1}8 + \ ^{7}C_{2}8^{2} + \ ^{7}C_{3}8^{3} + ... + \ ^{7}C_{7}8^{7}$
$\therefore\ 7^{9} + 9^{7} = 8\left( \ ^{9}C_{1} + \ ^{7}C_{1} \right) + 8^{2}\left( \ ^{7}C_{2} - \ ^{9}C_{2} \right) + \ldots$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 8(9 + 7) + 8^{2}(21 - 36) + \ldots$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 64 \times 2 + 64( - 15) + \ldots$
Hence, it is divisible by 64