A simple mathematics riddle that has me batty.

Good work.

To get a quick estimate without calculating it's useful to remember that $2^{10}$ is approximately $1000$ since it's exactly $1024$. Then $2^{20}$ is approximately $1000 \times 1000$ which is a million. Then $2^{23}$ is about $2^3 = 8$ times that, or $8$ million.