Solve x={5}^frac{5{5}}x{5}^frac{-y{z}}

$$x= { 5 }^{ \frac{ 5 }{ 5 } } x { 5 }^{ \frac{ -y }{ z } }$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&y=z\text{ and }z\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide 5 by 5 to get 1.

$$x=5^{1}x\times 5^{\frac{-y}{z}}$$

Calculate 5 to the power of 1 and get 5.

$$x=5x\times 5^{\frac{-y}{z}}$$

Subtract 5x\times 5^{\frac{-y}{z}} from both sides.

$$x-5x\times 5^{\frac{-y}{z}}=0$$

Reorder the terms.

$$x-5x\times 5^{-\frac{y}{z}}=0$$

Combine all terms containing x.

$$\left(1-5\times 5^{-\frac{y}{z}}\right)x=0$$

Divide 0 by 1-5\times 5^{-yz^{-1}}.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}y=z\text{, }&z\neq 0\\y\in \mathrm{R}\text{, }&x=0\text{ and }z\neq 0\end{matrix}\right.$$