For a positive integer \(n\), \(\phi(n)\)denotes the number of positive integers less than or equal to \(n\) that are relatively prime to \(n\). What is \(\phi(2^{100})\)?
\(\text{The odd numbers will be relatively prime to }2^{100} \\ \text{so }\phi(2^{100}) = \dfrac 1 2 2^{100} = 2^{99}\)