An algebra problem by Aly Ahmed

Algebra Level 2

\[\large A = \dfrac 1{2^3} + \dfrac 1{2^6} + \dfrac 1{2^9} + \cdots + \dfrac1{2^{3n}} + \cdots , \quad \quad B = \log_{128} 2 \]

Find \(B^{\log_A 4}\).

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