解決sqrt[3]{a^2*sqrt{a*sqrt[4]{asqrt{a}}}}=a^frac{x{9b}} |Microsoft數學求解器

$$\sqrt[ 3 ] { a ^ { 2 } \cdot \sqrt { a \cdot \sqrt[ 4 ] { a \sqrt { a } } } } = a ^ { \frac { x } { 9 b } }$$

解 a

$$\left\{\begin{matrix}a=0\text{, }&\left(x<0\text{ and }b<0\right)\text{ or }\left(x>0\text{ and }b>0\right)\\a=1\text{, }&b\neq 0\\a>0\text{, }&a>0\text{ and }x\neq 0\text{ and }b=\frac{16x}{129}\end{matrix}\right.$$

解 b

$$\left\{\begin{matrix}b=\frac{16x}{129}\text{, }&x\neq 0\text{ and }a\geq 0\\b\neq 0\text{, }&a=1\\b>0\text{, }&x>0\text{ and }a=0\\b<0\text{, }&x<0\text{ and }a=0\end{matrix}\right.$$