Divide $a^{7} b^{2}$ by $a^{2} b^{2}$

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Solution

There are two variable here, $a$ and $b$ . Thus we have to divide $a^{7}$ by $a^{2}$ and $b^{2}$ by $b^{2}$ . We obtain
$\frac{a^{7} b^{2}}{a^{2} b^{2}} = (\frac{a^{7}}{a^{2}}) (\frac{b^{2}}{b^{2}}) = a^{7 - 2} b^{2 - 2} = a^{5} b^{0} = a^{5}$ .
Note that we are following the convention $b^{0} = 1$ .

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