There are maybe two or more ways to achieve this, depending on what exactly you want. If you only want the path to change, and not the filename, you can use the find/replace feature of the RMC utility.
e.g. replace E:\Music\ with F:\Songs, and MC will reproduce the folder structure below E:\Music in F:\Songs. So the file
E:\Music\Abba\Swedish Twerk Compilation\Morning has Broken.mp3
will be moved to
F:\Songs\Abba\Swedish Twerk Compilation\Morning has Broken.mp3
However, if you have other files in those folders that are not in MC's library, or in the current view in Standard View, you would be better off to do the above but FIRST:
Select "Update Database..." for the first drop-down menu in RMC.
Then, manually move all your files to the new location within Windows.
MC will be looking for the files in the new location because you did "Update database..."