Is it always possible to convert a k-tape Turing machine to a single-tape one without increasing its running time complexity exponentially?

Question

I am studying the past exam paper of course Theory of Computation. I know it is always possible to convert a k-tape Turing machine to a single-tape one, but how will the running time complexity be changed?

Answer 1

It actually depends on the way you implement a k-tape Turing Machine as a single-tape one.

Using the standard implementation, you can prove that the single-tape machine will take quadratically more computation time.