We consider the Pure Safe Ambient Calculus, which is Levi and Sangiorgi's Safe Ambient Calculus (a variant of Cardelli and Gordon's Mobile Ambient Calculus) restricted to its mobility primitives – in particular, we focus on its expressive power. Since it has no form of communication or substitution, we show how these notions can be simulated by mobility and modifications in the hierarchical structure of ambients. As a main result, we use these techniques to design an encoding of the synchronous $\pi$-calculus into pure ambients, and we study its correctness, thus showing that pure ambients are as expressive as the $\pi$-calculus. In order to simplify the proof and give an intuitive understanding of the encoding, we design an intermediate language, the $\pi$-Calculus with Explicit Substitutions and Channels, which is an extension of the $\pi$-calculus in which communication and substitution are broken into simpler steps, and we show that is has the same expressive power as the $\pi$-calculus.