Question

$$\sqrt[3]{\frac{x}{a}}=b$$

Solve for a (complex solution)

$\left\{\begin{matrix}a=\frac{x}{b^{3}}\text{, }&x\neq 0\text{ and }arg(b)<\frac{2\pi }{3}\text{ and }b\neq 0\\a\neq 0\text{, }&b=0\text{ and }x=0\end{matrix}\right.$

Solve for a

$\left\{\begin{matrix}a=\frac{x}{b^{3}}\text{, }&x\neq 0\text{ and }b\neq 0\\a\neq 0\text{, }&b=0\text{ and }x=0\end{matrix}\right.$

Solve for b

$b=\sqrt[3]{\frac{x}{a}}$
$a\neq 0$