Final answer:
Polyadenylation and splicing both occur in the nucleus of a cell, where they are essential for modifying pre-mRNA into mature mRNA before it is transported to the cytoplasm for translation.
Step-by-step explanation:
Polyadenylation and splicing are processes involved in the post-transcriptional modification of pre-messenger RNA (pre-mRNA) and both occur within the nucleus of a cell. Specifically, polyadenylation involves the addition of a poly-A tail to the 3'-end of a transcript, and splicing involves the removal of introns and joining of exons in pre-mRNA. These processes are essential for converting pre-mRNA into mature mRNA, which is then transported out of the nucleus and into the cytoplasm where ribosomes translate it into protein.