How can a piece of music be rearranged while preserving its original themes?

The option that states changing the instrumentation and structure while preserving the core ideas is correct because it focuses on the essence of the original music while allowing for creativity in how those ideas are expressed. This rearranging can include altering the orchestration, dynamics, or even the form in which the music is presented, while still retaining the main themes, motifs, or harmonic progressions that define the original piece. This approach allows composers to explore new textures and colors while respecting the foundational elements of the music.

In contrast, the other options suggest changes that could compromise the integrity of the original themes. Altering the rhythm while keeping the melody intact can change the character of the piece significantly, potentially leading to a disconnect from the original themes. Composing entirely new verses diverges from rearranging since it involves the creation of new material rather than reinterpreting existing themes. Notating for a different genre could result in a completely different stylistic approach, possibly losing the original themes' essence in the process. Thus, the selected answer stands out as it embraces the core ideas while allowing for an innovative rearrangement.