Question

Carry out the following division: $\frac{12{\mathrm{a}}^8{\mathrm{b}}^8}{-6{\mathrm{a}}^6{\mathrm{b}}^6}$

Answer 1

Given, expression is

$\frac{12{\mathrm{a}}^8{\mathrm{b}}^8}{-6{\mathrm{a}}^6{\mathrm{b}}^6}$

$\begin{array}{rcl}\frac{12{\mathrm{a}}^8{\mathrm{b}}^8}{-6{\mathrm{a}}^6{\mathrm{b}}^6}& =& \frac{12}{-6}\times \frac{{\mathrm{a}}^8}{{\mathrm{a}}^6}\times \frac{{\mathrm{b}}^8}{{\mathrm{b}}^6}\\ & =& -2\times {\mathrm{a}}^{8-6}\times {\mathrm{b}}^{8-6}\left(\mathrm{Note}:\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\right)\\ & =& -2\times {\mathrm{a}}^2\times {\mathrm{b}}^2\\ & =& -2{\mathrm{a}}^2{\mathrm{b}}^2\end{array}$

Hence, $\frac{12{\mathrm{a}}^8{\mathrm{b}}^8}{-6{\mathrm{a}}^6{\mathrm{b}}^6}=-2{\mathrm{a}}^2{\mathrm{b}}^2$