TeX Quellcode:

\begin{array}{ccl} \left(x^{1{,}25} : y^{-0{,}625}\right)^{-\frac{4}{5}} &=& \left(x^{1{,}25} : \dfrac{1}{y^{0{,}625}}\right)^{-\frac{4}{5}} \cr\cr &=& \left( x^{1{,}25} \cdot y^{0{,}625} \right)^{-\frac{4}{5}} \cr\cr &=& x^{1{,}25 \cdot \left(-\frac{4}{5}\right)}\cdot y^{0{,}625\cdot\left(-\frac{4}{5}\right)} \cr \cr &=& x^{\frac{5}{4} \cdot \left(-\frac{4}{5}\right)}\cdot y^{\frac{5}{8}\cdot\left(-\frac{4}{5}\right)} \cr \cr &=& x^{-1} \cdot y^{-\frac{1}{2}} \cr\cr &=& \dfrac{1}{x^1 \cdot y^{\frac{1}{2}}} \cr\cr &=& \dfrac{1}{x\cdot \sqrt{y}} \cr\cr &=& \dfrac{\sqrt{y}}{x\cdot y} \end{array}