# finding grammar for language with 2^n same characters [duplicate]

Disclaimer: This is a homework question.
Given the language $$L=\{a^{2^n}| n\in\mathbb{N}\}$$:
1. find a corresponding grammar
2. give a derivation of $$a^{2^3}$$
3. In which Chomsky hierarchy is this language? arguments sufficient, no proof needed.