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: \(x = {1 \over { \sqrt[3]{16}}} = \color{brown}\boxed{2 \sqrt[3]{2}}\)