Answer
Makes sense.
Work Step by Step
Say the initial image has area $ A.$
1st reduction: area is now $(\displaystyle \frac{1}{2})A $
2nd reduction: area is now $(\displaystyle \frac{1}{2})[(\frac{1}{2})A ]=(\displaystyle \frac{1}{2})^{2}A $
3rd reduction: area is now $(\displaystyle \frac{1}{2})[(\frac{1}{2})^{2}A ]=(\displaystyle \frac{1}{2})^{3}A $
...
xth reduction: area is now $(\displaystyle \frac{1}{2})^{x}A $
Makes sense.
