${\displaystyle \frac{2\cdot x^5\cdot \mathrm{0,5}\cdot y^{-3}\cdot 4x^3\cdot 2\cdot y}{8\cdot y^{-2}\cdot x^7}}+{\displaystyle \frac{x^{\frac{3}{2}}}{\sqrt{x}}}\backslash dfrac\{2\backslash cdot\; x^5\backslash cdot0\{,\}5\backslash cdot\; y^\{-3\}\backslash cdot4x^3\backslash cdot2\backslash cdot\; y\}\{8\backslash cdot\; y^\{-2\}\backslash cdot\; x^7\}+\backslash dfrac\{x^\{\backslash frac\{3\}\{2\}\}\}\{\backslash sqrt\{x\}\}$

$\text{ordne und schreibe die Wurzel im Nenner als Potenz}\backslash text\{\backslash color\{green\}\{ordne\backslash \; \backslash text\{und\; schreibe\; die\; Wurzel\; im\; Nenner\; als\; Potenz\}\}\}$

${\displaystyle \frac{\mathrm{0,5}\cdot 2\cdot 2\cdot 4\cdot (x^5\cdot x^3)\cdot (y\cdot y^{-3})}{8\cdot x^7\cdot y^{-2}}}+{\displaystyle \frac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}}\backslash dfrac\{0\{,\}5\backslash cdot2\backslash cdot2\backslash cdot4\backslash cdot(x^5\backslash cdot\; x^3)\backslash cdot(y\backslash cdot\; y^\{-3\})\}\{8\backslash cdot\; x^7\backslash cdot\; y^\{-2\}\}+\backslash dfrac\{x^\{\backslash frac\{3\}\{2\}\}\}\{x^\{\backslash frac\{1\}\{2\}\}\}$

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

${\displaystyle \frac{\cancel{\mathrm{0,5}}\cdot \cancel{2}\cdot \cancel{2}\cdot \cancel{4}\cdot (x^5\cdot x^3)\cdot (y\cdot y^{-3})}{\cancel{8}\cdot x^7\cdot y^{-2}}}+{\displaystyle \frac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}}\backslash dfrac\{\backslash cancel\{0\{,\}5\}\backslash cdot\backslash cancel\{\backslash \; 2\}\backslash cdot\backslash cancel\{\backslash \; 2\}\backslash cdot\backslash cancel\{\backslash \; 4\}\backslash cdot(x^5\backslash cdot\; x^\{3\})\backslash cdot(\; y\backslash cdot\; y^\{-3\})\}\{\backslash cancel\{\backslash \; 8\}\backslash cdot\; x^\{7\}\backslash cdot\; y^\{-2\}\}+\backslash dfrac\{x^\{\backslash frac\{3\}\{2\}\}\}\{x^\{\backslash frac\{1\}\{2\}\}\}$

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

${\displaystyle \frac{(x^5\cdot x^3)\cdot (y\cdot y^{-3})}{x^7\cdot y^{-2}}}+{\displaystyle \frac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}}\backslash dfrac\{(x^5\backslash cdot\; x^\{3\})\backslash cdot(\; y\backslash cdot\; y^\{-3\})\}\{x^\{7\}\backslash cdot\; y^\{-2\}\}+\backslash dfrac\{x^\{\backslash frac\{3\}\{2\}\}\}\{x^\{\backslash frac\{1\}\{2\}\}\}$

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

$(x^{5+3-7})\cdot (y^{1+(-3)-(-2)})+x^{(\frac{3}{2}-\frac{1}{2})}\{(x^\{5+3-7\})\backslash cdot(\; y^\{1+(-3)-(-2)\})\}+x^\{(\{\backslash frac\{3\}\{2\}\}-\backslash frac\{1\}\{2\})\}$

$x^1\cdot y^0+x^{\frac{2}{2}}\backslash hspace\{2mm\}x^1\backslash hspace\{6.8mm\}\backslash cdot\; \backslash hspace\{1.8mm\}y^0\backslash hspace\{14.5mm\}+x^\{\backslash frac\{2\}\{2\}\}$

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