$({\mathrm{a}}^2\cdot {\mathrm{b}}^2{)}^{\frac{1}{2}}={\mathrm{a}}^{2\cdot \frac{1}{2}}\cdot {\mathrm{b}}^{2\cdot \frac{1}{2}}=\mathrm{a}\cdot \mathrm{b}\backslash mathrm\{(a^2\backslash cdot\; b^2)^\backslash frac\{1\}\{2\}\; =\; a^\{2\backslash cdot\; \backslash frac\{1\}\{2\}\}\backslash cdot\; b^\{2\backslash cdot\; \backslash frac\{1\}\{2\}\}\; =\; a\backslash cdot\; b\}$

${\mathrm{s}}^{-2}\cdot {\mathrm{t}}^2\mathrm{\ne }{\mathrm{s}}^2\cdot {\mathrm{t}}^2=(\mathrm{s}\cdot \mathrm{t}{)}^2\backslash mathrm\{s^\{-2\}\backslash cdot\; t^2\; \backslash neq\; s^2\backslash cdot\; t^2\; =(s\backslash cdot\; t)^2\}$

${\displaystyle \frac{{\mathrm{x}}^2}{{\mathrm{y}}^{-2}}}={\mathrm{x}}^2\cdot {\mathrm{y}}^2=(\mathrm{x}\cdot \mathrm{y}{)}^2\backslash mathrm\{\backslash dfrac\{x^2\}\{y^\{-2\}\}=x^2\backslash cdot\; y^2=(x\backslash cdot\; y)^2\}$