2 ^ 10 = 1024.

That's one of those "shout it from the rooftops" approximations for programmers. I use it constantly.

And this is why base-ten and base-two file and memory sizes are roughly equivalent (which is somewhat useful but also causes a lot of confusion):

    2^10 bytes = 1 kiB ≈ 1 kB = 10^3 bytes
    2^20 bytes = 1 MiB ≈ 1 MB = 10^6 bytes
    2^30 bytes = 1 GiB ≈ 1 GB = 10^9 bytes
    2^40 bytes = 1 TiB ≈ 1 TB = 10^12 bytes

and so on. The relative error does grow as you move to larger and larger powers, though.

As the other answers point out, it follows from explicit computation. Let me add that there's no particularly good a priori reason to expect this particular coincidence. It just happens.

Compare 1000 with 1024.

As I say above, 2^10 is bigger than 10^3 by 2.4%. When we raise it to the power of 5 we are wrong by 12.6%.