Simplify: ${\left(-3\right)}^2÷a^2$

Given: ${\left(-3\right)}^2÷a^2$

We know, the law of exponents,

${\mathrm{a}}^{\mathrm{m}}÷{\mathrm{b}}^{\mathrm{m}}=\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{b}}^{\mathrm{m}}}={\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{\mathrm{m}}$

Therefore, ${\left(-3\right)}^2÷a^2=\frac{{\left(-3\right)}^2}{a^2}={\left(\frac{-3}{a}\right)}^2$

Now the expression ${\left(\frac{-3}{a}\right)}^2$ can be written as,

${\left(\frac{-3}{a}\right)}^2={\left(-1\right)}^2\times {\left(\frac{3}{a}\right)}^2$

$\Rightarrow {\left(\frac{-3}{a}\right)}^2={\left(\frac{3}{a}\right)}^2$     [$\because {\left(-1\right)}^{\mathrm{even} \mathrm{number}}=1$]

Thus, ${\left(-3\right)}^2÷a^2={\left(\frac{3}{a}\right)}^{\mathbf{2}}$