Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{3}^{2}{({a}^{2})}^{2}}{18{a}^{3}}\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{9{({a}^{2})}^{2}}{18{a}^{3}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{9{a}^{4}}{18{a}^{3}}\]
Take out the constants.
\[\frac{9}{18}\times \frac{{a}^{4}}{{a}^{3}}\]
Simplify \(\frac{9}{18}\) to \(\frac{1}{2}\).
\[\frac{1}{2}\times \frac{{a}^{4}}{{a}^{3}}\]
Simplify.
\[\frac{{a}^{4}}{2{a}^{3}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[\frac{{a}^{4-3}}{2}\]
Simplify \(4-3\) to \(1\).
\[\frac{{a}^{1}}{2}\]
Use Rule of One: \({x}^{1}=x\).
\[\frac{a}{2}\]
a/2
