why is 2^8, 256 and not 512?

[NickThissen]

Easy way to visualise it:

n⁰ = 1
n¹ = n
n² = nn
n³ = nnn
n⁴ = nnnn
n^k = nnnnn...[k]

Just to add to this:

n^-1 = 1 / n
n^-2 = 1 / (nn)
n^-3 = 1 / (nnn)
n^-x = 1 / (nnnnn ... [x])