${\displaystyle \frac{2\cdot x^3\cdot 6\cdot y^{-4}\cdot 10\cdot z^{-6}\cdot x^{-2}\cdot 2\cdot y^8\cdot z^2}{3\cdot y^2\cdot 10\cdot x^{-3}\cdot 4\cdot z^{-4}}}\backslash dfrac\{2\backslash cdot\; x^3\backslash cdot6\backslash cdot\; y^\{-4\}\backslash cdot10\backslash cdot\; z^\{-6\}\backslash cdot\; x^\{-2\}\backslash cdot2\backslash cdot\; y^8\backslash cdot\; z^2\}\{3\backslash cdot\; y^2\backslash cdot10\backslash cdot\; x^\{-3\}\backslash cdot4\backslash cdot\; z^\{-4\}\}$

$\text{ordne}\backslash text\{\backslash color\{green\}\{ordne\}\}$

${\displaystyle \frac{2\cdot 2\cdot 6\cdot 10\cdot (x^3\cdot x^{-2})\cdot (y^8\cdot y^{-4})\cdot (z^2\cdot z^{-6})}{3\cdot 4\cdot 10\cdot x^{-3}\cdot y^2\cdot z^{-4}}}\backslash dfrac\{2\backslash cdot2\backslash cdot6\backslash cdot10\backslash cdot(x^3\backslash cdot\; x^\{-2\})\backslash cdot(y^8\backslash cdot\; y^\{-4\})\backslash cdot(z^2\backslash cdot\; z^\{-6\})\}\{3\backslash cdot4\backslash cdot10\backslash cdot\; x^\{-3\}\backslash cdot\; y^2\backslash cdot\; z^\{-4\}\}$

$\text{k}\ddot{\text{u}}\text{rze}\backslash text\{\backslash color\{green\}\{kürze\}\}$

${\displaystyle \frac{\cancel{2}\cdot \cancel{2}\cdot \cancel{6}2\cdot \cancel{10}\cdot (x^3\cdot x^{-2})\cdot (y^8\cdot y^{-4})\cdot (z^2\cdot z^{-6})}{\cancel{3}\cdot \cancel{4}\cdot \cancel{10}\cdot x^{-3}\cdot y^2\cdot z^{-4}}}\backslash dfrac\{\backslash cancel\{2\backslash \; \}\backslash cdot\; \backslash cancel\{2\backslash \; \}\backslash cdot\backslash cancel\{6\backslash \; \}\backslash \; 2\backslash cdot\; \backslash cancel\{10\}\backslash cdot\; (x^\{3\}\backslash cdot\; x^\{-2\})\backslash cdot\; (y^8\backslash cdot\; y^\{-4\})\backslash cdot(z^2\backslash cdot\; z^\{-6\})\}\{\backslash cancel\{3\backslash \; \}\backslash cdot\; \backslash cancel\{4\backslash \; \}\backslash cdot\; \backslash cancel\{10\}\backslash cdot\; x^\{-3\}\backslash cdot\; y^\{2\}\backslash cdot\; z^\{-4\}\}$

$\text{fasse zusammen}\backslash text\{\backslash color\{green\}\{fasse\; zusammen\}\}$

${\displaystyle \frac{2\cdot (x^3\cdot x^{-2})\cdot (y^8\cdot y^{-4})\cdot (z^2\cdot z^{-6})}{x^{-3}\cdot y^2\cdot z^{-4}}}\backslash dfrac\{2\backslash cdot\; (x^\{3\}\backslash cdot\; x^\{-2\})\backslash cdot\; (y^8\backslash cdot\; y^\{-4\})\backslash cdot(z^2\backslash cdot\; z^\{-6\})\}\{x^\{-3\}\backslash cdot\; y^\{2\}\backslash cdot\; z^\{-4\}\}$

$\text{vereinfache}\backslash text\{\backslash color\{green\}\{vereinfache\}\}$

$2\cdot x^{(3+3-2)}\cdot y^{(8-4-2)}\cdot z^{(4-4)}2\backslash cdot\; x^\{(3+3-2)\}\backslash cdot\; y^\{(8-4-2)\}\backslash cdot\; z^\{(4-4)\}$

$\text{Vereinfachter Term: }\Rightarrow 2x^4{y}^2\backslash text\{\{Vereinfachter\; Term:\}\}\backslash \; \backslash Rightarrow\backslash \; 2x^4y^2$