Solve (a^x)(a^y)=a^8

$$( a ^ { x } ) ( a ^ { y } ) = a ^ { 8 }$$

Solve for a

$$\left\{\begin{matrix}\\a=1\text{, }&\text{unconditionally}\\a=0\text{, }&x>0\text{ and }y>0\\a=-1\text{, }&Numerator(x+y)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }Denominator(y)\text{bmod}2=1\\a>0\text{, }&x=8-y\\a<0\text{, }&y=8-x\text{ and }Denominator(x)\text{bmod}2=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=8-y\text{, }&a>0\text{ or }\left(Denominator(y)\text{bmod}2=1\text{ and }a<0\right)\\x\in \mathrm{R}\text{, }&a=1\text{ or }\left(Numerator(x)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }Numerator(8-y)\text{bmod}2=1\text{ and }Denominator(y)\text{bmod}2=1\text{ and }a=-1\right)\text{ or }\left(Numerator(x)\text{bmod}2=0\text{ and }Numerator(8-y)\text{bmod}2=0\text{ and }Denominator(y)\text{bmod}2=1\text{ and }a=-1\text{ and }Denominator(x)\text{bmod}2=1\right)\\x>0\text{, }&a=0\text{ and }y>0\end{matrix}\right.$$