Using induction on i, prove that 〖〖(w〗^R)〗^i=〖〖(w〗^i)〗^R for any string w and all i 0. Hints: feel free to use the following Theorem in your proof Let u,v∈Σ^*, then 〖(uv)〗^R=v^R u^R.
Using induction on i, prove that 〖〖(w〗^R)〗^i=〖〖(w〗^i)〗^R for any string w and all i 0....