An algebra problem by Saksham Jain

Algebra Level 2

Let \(A\) denote the sum of an infinite geometric progression, \( \dfrac1{2^3} + \dfrac1{2^6} + \dfrac1{2^9} + \cdots \).

Let \(B = \log_{128}2 \), compute \(\Large B^{\log_A 4 } \).