Final answer:
The term for expanding a worker's role to include more responsibilities with decision-making power is 'job enrichment'.
Step-by-step explanation:
The term for a worker's role being expanded to include additional responsibilities over which they have some decision-making power is job enrichment. This concept involves not only increasing the range of tasks for an employee but also providing them with more autonomy and control over their work. This approach to job design is aimed at increasing job satisfaction and motivation by allowing workers to use more of their skills and abilities, which in turn can lead to improved performance.
In contrast, 'job enlargement' refers to simply increasing the number of tasks without necessarily giving more control to the employee. 'Job expansion' and 'job extension' are terms less commonly used in the context of job design and do not precisely describe the addition of decision-making power to a worker's responsibilities.