Useful root property: $\frac{\sqrt[n]{x}}{\sqrt[n]{y}}=\sqrt[n]{\frac{x}{y}}$

Given: $(\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})$

Divide both sides by $\sqrt{5.5}$ to get: $\sqrt[3]{4}=\frac{(\sqrt{22})(\sqrt[3]{x})}{\sqrt{5.5}}$

Divide both sides by $\sqrt[3]{x}$ to get: $\frac{\sqrt[3]{4}}{\sqrt[3]{x}}=\frac{\sqrt{22}}{\sqrt{5.5}}$

Apply above property to both sides to get: $\sqrt[3]{\frac{4}{x}}=\sqrt{\frac{22}{5.5}}$

Simplify right side: $\sqrt[3]{\frac{4}{x}}=\sqrt{4}$

Simplify right side: $\sqrt[3]{\frac{4}{x}}=2$

Raise both sides to the power of 3 to get: $(\sqrt[3]{\frac{4}{x}})^3=2^3$

Simplify: $\frac{4}{x} = 8$

Solve: $x = \frac{4}{8} = \frac{1}{2}$

Answer: B

Cheers,
Brent