14. (i) 6 ; (ii) $2^{22} \equiv 4(\bmod 100), 2^{1000} \equiv 2^{100} \equiv 2^{20} \equiv 76(\bmod 100), 76$;
(iii) $9^{10}$ $\equiv(10-1)^{10} \equiv 1(\bmod 100), 9^{9} \equiv(10-1)^{9} \equiv 9(\bmod 10)$, so $9^{9^{9}} \equiv 9^{9} \equiv -11 \equiv$ $89(\bmod 100)$, the last two digits are $89, 9^{9^{9}} \equiv 9^{89} \equiv 9^{9} \equiv 89(\bmod 100)$, the last two digits are also 89 ; (iv) 70 ; (v) 6.
14. (i) Find the least non-negative residue of $2^{400}$ modulo 10;
(ii) Find the last two digits in the decimal representation of $2^{1000}$;
(iii) Find the last two digits in the decimal representation of $9^{9^{9}}$ and $9^{9^{9^{9}}}$;
(iv) Find the least non-negative residue of $\left(13481^{56}-77\right)^{28}$ when divided by 111;
(v) Find the least non-negative residue of $2^{s}$ modulo 10, where $s=2^{k}, k \geqslant 2$.