There is a popular legend which states that, communication is not complete until there is a corresponding response.
When someone sends you an email either officially or personally, asking you to perform tasks, send them feedback that you received their mail, and that you will work on the tasks as soon as possible. When you are done with the tasks, follow through by sending another email that you have completed the tasks. This way everybody will be informed on the latest about the task.
This act is not only professional, it is also a courteous and priceless act, and it can propel you forward to that place you so desire in a short period. Correct?