While Putin often shows a flair for being able to speak on almost any subject at all, off the cuff, I picked this clip from 2012 to showcase this. During this meeting, Putin faced some criticism in relation to his choice of a Prime Minister - Dmitry Medvedev. As you may recall, Medvedev was President between 2008 and 2012, so the two simply swapped seats.
Whatever your opinion is on this - I stick to the age old adage, that if you wan't something done right, you gotta do it yourself [and your established team]. Putin was also fully within his Presidential powers to appoint his own Prime Minister, and the appointed government is then also approved by parliament.
In this outtake during a Duma meeting, Putin answers a number of questions that were thrown at him by members of Opposition parties, and leaves with nothing less than an ovation.