TeX Quellcode:

\begin{array}{ccl} \sqrt[5]{\dfrac{\sqrt[4]{\left(a^4b^2\right)^{10}}}{\sqrt{a^{10}b^5}}} &=& \sqrt[5]{\dfrac{\sqrt[4]{a^{40}b^{20}}}{\sqrt{a^{10}b^5}}} \cr \cr &=& \sqrt[5]{\dfrac{a^{40\cdot \frac{1}{4}}b^{20 \cdot \frac{1}{4}}}{a^{10 \cdot \frac{1}{2}}b^{5 \cdot \frac{1}{2}}}} \cr \cr &=& \sqrt[5]{\dfrac{a^{10}b^5}{a^5b^\frac{5}{2}}} \cr \cr &=& \dfrac{a^{10 \cdot \frac{1}{5}}b^{5 \cdot \frac{1}{5}}}{a^{5 \cdot \frac{1}{5}}b^{\frac{5}{2} \cdot \frac{1}{5}}} \cr \cr &=& \dfrac{a^2b}{ab^\frac{1}{2}} \cr \cr &=& a^2ba^{-1}b^{-\frac{1}{2}} \cr &=& a^{2-1}b^{1-\frac{1}{2}} \cr &=& ab^\frac{1}{2} \cr &=& a\sqrt{b} \end{array}