$\backslash$${\displaystyle \frac{21x^{-4}\cdot 9y^3\cdot 6z^5\cdot x^3\cdot 8z^{-8}}{4y^2\cdot 7x^{-6}\cdot 3y\cdot 18z^{-4}}}\backslash dfrac\{21x^\{-4\}\backslash cdot\; 9y^3\backslash cdot\; 6z^5\backslash cdot\; x^3\backslash cdot\; 8z^\{-8\}\}\{4y^2\backslash cdot\; 7x^\{-6\}\backslash cdot\; 3y\backslash cdot\; 18z^\{-4\}\}$

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

${\displaystyle \frac{21\cdot 9\cdot 6\cdot 8\cdot x^3\cdot x^{-4}\cdot y^3\cdot z^5\cdot z^{-8}}{4\cdot 7\cdot 3\cdot 18\cdot x^{-6}\cdot y^2\cdot y\cdot z^{-4}}}\backslash dfrac\{21\backslash cdot\; 9\backslash cdot\; 6\backslash cdot\; 8\backslash cdot\; x^3\backslash cdot\; x^\{-4\}\backslash cdot\; y^3\backslash cdot\; z^5\backslash cdot\; z^\{-8\}\}\{4\backslash cdot\; 7\backslash cdot\; 3\backslash cdot\; 18\backslash cdot\; x^\{-6\}\backslash cdot\; y^2\backslash cdot\; y\backslash cdot\; z^\{-4\}\; \}$

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

${\displaystyle \frac{\cancel{21}\cdot \cancel{9}\cdot 6\cdot \cancel{8}\cdot x^3\cdot x^{-4}\cdot y^3\cdot z^5\cdot z^{-8}}{\cancel{4}\cdot \cancel{7}\cdot \cancel{3}\cdot \cancel{18}\cdot x^{-6}\cdot y^2\cdot y\cdot z^{-4}}}\backslash dfrac\{\backslash cancel\{21\}\backslash cdot\; \backslash cancel\{9\backslash \; \}\backslash cdot\; 6\backslash cdot\; \backslash cancel\{8\backslash \; \}\backslash cdot\; x^3\backslash cdot\; x^\{-4\}\backslash cdot\; y^3\backslash cdot\; z^5\backslash cdot\; z^\{-8\}\}\{\backslash cancel\{4\backslash \; \}\backslash cdot\; \backslash cancel\{7\backslash \; \}\backslash cdot\; \backslash cancel\{3\backslash \; \}\backslash cdot\; \backslash cancel\{18\}\backslash cdot\; x^\{-6\}\backslash cdot\; y^2\backslash cdot\; y\backslash cdot\; z^\{-4\}\; \}$

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

${\displaystyle \frac{6\cdot (x^3\cdot x^{-4})\cdot y^3\cdot (z^5\cdot z^{-8})}{x^{-6}\cdot (y^2\cdot y)\cdot z^{-4}}}\backslash dfrac\{6\; \backslash cdot\; \backslash left(x^3\backslash cdot\; x^\{-4\}\backslash right)\backslash cdot\; y^3\backslash cdot\; \backslash left(z^5\backslash cdot\; z^\{-8\}\backslash right)\}\{x^\{-6\}\backslash cdot\; \backslash left(y^2\backslash cdot\; y\backslash right)\backslash cdot\; z^\{-4\}\}$

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

$6\cdot x^{(3-4+6)}\cdot y^{(3-3)}\cdot z^{(5-8+4)}6\; \backslash cdot\; x^\{(3-4+6)\}\backslash cdot\; y^\{(3-3)\}\backslash cdot\; z^\{(5-8+4)\}$

$\text{Vereinfachter Term: }\Rightarrow \boxed{{\displaystyle 6x^{5}z}}\backslash text\{\{Vereinfachter\; Term:\}\}\backslash \; \backslash Rightarrow\backslash \; \backslash boxed\{6x^5z\}$