$\left\{\begin{matrix}a=b^{\frac{1}{x}}\text{, }&x\neq 0\text{ and }b\neq 1\text{ and }b>0\text{ and }b^{\frac{1}{x}}-1\neq 0\\a\in \left(0,1\right)\cup \left(1,\infty\right)\text{, }&b=1\text{ and }x=0\end{matrix}\right.$

$b=a^{x}$
$a\neq 1\text{ and }a>0$