Divide:  $({\mathrm{p}}^3{\mathrm{q}}^6-{\mathrm{p}}^6{\mathrm{q}}^3)$ by ${\mathrm{p}}^3{\mathrm{q}}^3$.

$({\mathrm{p}}^3{\mathrm{q}}^6-{\mathrm{p}}^6{\mathrm{q}}^3)÷{\mathrm{p}}^3{\mathrm{q}}^3$

$=\frac{{\mathrm{p}}^3{\mathrm{q}}^6-{\mathrm{p}}^6{\mathrm{q}}^3}{{\mathrm{p}}^3{\mathrm{q}}^3}$

$=\frac{{\mathrm{p}}^3{\mathrm{q}}^6}{{\mathrm{p}}^3{\mathrm{q}}^3}-\frac{{\mathrm{p}}^6{\mathrm{q}}^3}{{\mathrm{p}}^3{\mathrm{q}}^3}$

$=\frac{\cancel{{\mathrm{p}}^3\times }\mathrm{q}\times \mathrm{q}\times \mathrm{q}\times \cancel{\mathrm{q}}\times \cancel{\mathrm{q}}\times \cancel{\mathrm{q}}}{\cancel{{\mathrm{p}}^3\times }\cancel{\mathrm{q}}\times \cancel{\mathrm{q}}\times \cancel{\mathrm{q}}}-\frac{\cancel{\mathrm{p}}\times \cancel{\mathrm{p}}\times \cancel{\mathrm{p}}\times \mathrm{p}\times \mathrm{p}\times \mathrm{p}\times \cancel{{\mathrm{q}}^3}}{\cancel{\mathrm{p}}\times \cancel{\mathrm{p}}\times \cancel{\mathrm{p}}\times \cancel{{\mathrm{q}}^3}}$

$={\mathrm{q}}^3-{\mathrm{p}}^3$

Hence, when $({\mathrm{p}}^3{\mathrm{q}}^6-{\mathrm{p}}^6{\mathrm{q}}^3)$ is divided by ${\mathrm{p}}^3{\mathrm{q}}^3$, we get ${\mathrm{q}}^3-{\mathrm{p}}^3$.