Dienes blocks in the context of "Power of two"

A power of two is a number of the form 2 where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. In the fast-growing hierarchy, 2 is exactly equal to ${\displaystyle f_{1}^{n}(1)}$. In the Hardy hierarchy, 2 is exactly equal to ${\displaystyle H_{\omega {n}}(1)}$.

Powers of two with non-negative exponents are integers: 2 = 1, 2 = 2, and 2 is two multiplied by itself n times. The first ten powers of 2 for non-negative values of n are: