Algebra

Simplifying the left hand side gives 32x^3 = 2.

DIviding by 32 on both sides and taking cube root gives the answer.

Answer: $x = \dfrac1{2\sqrt[3]2}$

We have: $32x^3 = 2$

Dividing both sides by 32, we get: $x^3={1 \over 16}$

Taking the cube root of both sides, we have: $x = {1 \over { \sqrt[3]{16}}} = \color{brown}\boxed{2 \sqrt[3]{2}}$