Question

$${ \left( \sqrt{ \sqrt{ \sqrt{ \frac{ 1 }{ 64 } } } } - \frac{ 2 }{ 3 } \right) }^{ -1 }$$

Evaluate

$\frac{-81\times 2^{\frac{3}{4}}-108\sqrt{2}-144\sqrt[4]{2}-192}{47}\approx -13.876725714$

Factor

$-\frac{6 {(9 \sqrt{2} + 16)} {(2 ^ {\frac{7}{4}} + 3)}}{47 \cdot 2 ^ {\frac{3}{4}}} = -13.876725714208254$