Vereinfachen des Terms.

${\displaystyle \frac{9{\mathrm{x}}^{-2}\mathrm{y}\cdot 4{\mathrm{y}}^2{\mathrm{z}}^{-3}\cdot 5{\mathrm{x}}^7{\mathrm{y}}^{-1}\mathrm{z}}{2{\mathrm{y}}^2\cdot 3{\mathrm{x}}^{-2}{\mathrm{y}}^{-1}\cdot 2{\mathrm{x}}^1{\mathrm{z}}^{-2}}}\backslash mathrm\{\backslash dfrac\{9x^\{-2\}y\backslash cdot4y^2z^\{-3\}\backslash cdot5x^7y^\{-1\}z\}\{2y^2\backslash cdot3x^\{-2\}y^\{-1\}\backslash cdot2x^1z^\{-2\}\}\}$

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

${\displaystyle \frac{9\cdot 4\cdot 5\cdot {\mathrm{x}}^7\cdot {\mathrm{x}}^{-2}\cdot {\mathrm{y}}^2\cdot \mathrm{y}\cdot {\mathrm{y}}^{-1}\cdot \mathrm{z}\cdot {\mathrm{z}}^{-3}}{2\cdot 2\cdot 3\cdot \mathrm{x}\cdot {\mathrm{x}}^{-2}\cdot {\mathrm{y}}^2\cdot {\mathrm{y}}^{-1}\cdot {\mathrm{z}}^{-2}}}\backslash mathrm\{\backslash displaystyle\backslash frac\{9\backslash cdot4\backslash cdot5\backslash cdot\; x^7\backslash cdot\; x^\{-2\}\backslash cdot\; y^2\backslash cdot\; y\backslash cdot\; y^\{-1\}\backslash cdot\; z\backslash cdot\; z^\{-3\}\}\{2\backslash cdot2\backslash cdot3\backslash cdot\; x\backslash cdot\; x^\{-2\}\backslash cdot\; y^2\backslash cdot\; y^\{-1\}\backslash cdot\; z^\{-2\}\}\}$

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

${\displaystyle \frac{\cancel{9}3\cdot 5\cdot \cancel{4}\cdot {\mathrm{x}}^7\cdot {\mathrm{x}}^{-2}\cdot {\mathrm{y}}^2\cdot \mathrm{y}\cdot {\mathrm{y}}^{-1}\cdot \mathrm{z}\cdot {\mathrm{z}}^{-3}}{\cancel{2}\cdot \cancel{2}\cdot \cancel{3}\cdot \mathrm{x}\cdot {\mathrm{x}}^{-2}\cdot {\mathrm{y}}^2\cdot {\mathrm{y}}^{-1}\cdot {\mathrm{z}}^{-2}}}\backslash mathrm\{\backslash dfrac\{\backslash cancel\{9\}\backslash \; \{3\}\backslash cdot\; 5\backslash cdot\; \backslash cancel\{4\}\backslash cdot\; x^7\backslash cdot\; x^\{-2\}\backslash cdot\; y^2\backslash cdot\; y\backslash cdot\; y^\{-1\}\backslash cdot\; z\backslash cdot\; z^\{-3\}\}\{\backslash cancel\{2\}\backslash cdot\; \backslash cancel\{2\}\backslash cdot\; \backslash cancel\{3\}\backslash cdot\; x\backslash cdot\; x^\{-2\}\backslash cdot\; y^2\backslash cdot\; y^\{-1\}\backslash cdot\; z^\{-2\}\}\}$

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

${\displaystyle \frac{15\cdot \left({\mathrm{x}}^{7-2}\right)\cdot \left({\mathrm{y}}^{2+1-1}\right)\cdot \left({\mathrm{z}}^{1-3}\right)}{\left({\mathrm{x}}^{1-2}\right)\cdot \left({\mathrm{y}}^{2-1}\right)\cdot {\mathrm{z}}^{-2}}}\backslash mathrm\{\backslash displaystyle\backslash frac\{15\backslash cdot\backslash left(x^\{7-2\}\backslash right)\backslash cdot\backslash left(y^\{2+1-1\}\backslash right)\backslash cdot\backslash left(z^\{1-3\}\backslash right)\}\{\backslash left(x^\{1-2\}\backslash right)\backslash cdot\backslash left(y^\{2-1\}\backslash right)\backslash cdot\; z^\{-2\}\}\}$

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

$15\cdot {\mathrm{x}}^{(7-2+1)}\cdot {\mathrm{y}}^{(2-1)}\cdot {\mathrm{z}}^{(-2+2)}\backslash mathrm\{15\backslash cdot\; x^\{(7-2+1)\}\backslash cdot\; y^\{(2-1)\}\backslash cdot\; z^\{(-2+2)\}\}$

$\text{Vereinfachter Term: }\Rightarrow \boxed{{\displaystyle 15{\mathrm{x}}^6\mathrm{y}}}\backslash text\{\{Vereinfachter\; Term:\}\}\backslash \; \backslash Rightarrow\backslash \; \backslash boxed\{\backslash mathrm\{15x^6y\}\}$