What exactly does 'extensive participation' mean?
Can I use this phrase in a sentence like this:
Due to her extensive participation she hardly got time for her studies.
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There is no intrinsic problem with the phrase extensive participation. It is only meaningful in your sentence, however, if it is already clear (or is made explicit) to the listener or reader what the participation is in. For example:
Due to her extensive participation in the school's sports program she hardly has/had time for her studies.
In such a context, extensive participation would mean that she is/was involved in many different sports.