For length 1 string w = a

(a^{R})(a^{R})...(for k times)=(aa...(for k times))^{R}

For length 2 string w = ab

(ab^{R})(ab^{R})...(for k times)=(abab...(for k times))^{R}

babababababab..ba = babababababa..ba

so for string for length k

(w^{R})(w^{R})...(for k times)=(ww...(for k times))^{R}