Step 1 :Given that the student can shovel the driveway in 16 minutes, his rate of work is \(\frac{1}{16}\) driveways per minute.
Step 2 :Similarly, the brother can shovel the driveway in 14 minutes, so his rate of work is \(\frac{1}{14}\) driveways per minute.
Step 3 :The combined rate of work when they shovel together is the sum of their individual rates, which is \(\frac{1}{16} + \frac{1}{14} = 0.13392857142857142\) driveways per minute.
Step 4 :The time it will take them to shovel the driveway together is the reciprocal of their combined rate, which is \(\frac{1}{0.13392857142857142} = 7.466666666666667\) minutes.
Step 5 :Rounding to one decimal place, it will take approximately \(\boxed{7.5}\) minutes to clear the driveway together.