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Kranz's power as a leader originates from his position within the organisation's structure and hierarchy.
In this extremely stressful situation and Gene is saying: "Let's stay cool people! Let's work the problem, people, let's not make things worse by guessing" 
leaders must have the ability to make the final decision and exploit their power to put this decision into action. In this incidence, the specialists provide various suggestions and solutions on how to bring the astronauts back home, they argue and even strongly raise objections to one another's points of view, but Kranz has the final word and makes the decision based on his prompt evaluation of the information provided.
Taken from the bases outlined by French & Raven (1958), the power held by Kranz can be said to come mainly from the belief that he has sought-after skills and personal characteristics that can and should be emulated (Referent Power); the belief that he has authority to give out orders which they are obligated to follow due to his position within the formal organisation structure (Legitimate Power) and the belief that he has higher knowledge related to the present situation and mission (Expert Power). Since these bases are prone to change over time, Kranz's "expert power" is likely to increase due to the success of this mission.

About 58 minutes into the movie. One of Gene's followers suggests shutting down fuel cells in order to stop the leak. Gene realizes that this decision would determine if Apollo13 would make it to the moon. 
Gene Kranz and his subordinate (the engineer with big, black glasses)
After hearing the opinion of the engineer, Gene realizes that his decision will determine the success of the mission. He has developed a relationship with the engineer and trusts his judgment; therefore, making it easier for him to make the harsh decision. This situation also shows that Gene appreciates his subordinate's opinions and considers them as a major contributor to his success as a leader.

Ken's character was very much associated with Theory Y. He encouraged those around him to keep on working, but did not feel like he needed to control them. He used many methods of motivation to find solution. The people he worked with also seemed to enjoy their work. You could tell from their dedication that they were not there just for a paycheck. They were committed and motivated to help the team lost in space. 
Influencing - Ken influences the team to keep trying when it seems there is no solution in sight. He believes that an answer is near, so he encourages himself and others to be creative. He persuades the team to use the simulation shuttle in order to accomplish their goal.
Jack in a way motivates Ken to take responsibility and confidence to guide him through the procedure, as he has lost his eye focus. This situation is interesting, because in a way both, Jack and Ken take roles of leader and follower. They both influence each other moves and accomplish the goal that was set for them. About 14 minutes into the movie. Apollo 13 main crew has just finished their 7 hour practice simulation. Project coordinator approaches and congratulates the crew on a well done job.