Since the power of 4 is even, the result will be positive.
\[{(3{a}^{2})}^{4}{(2{a}^{6})}^{2}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{3}^{4}{({a}^{2})}^{4}{(2{a}^{6})}^{2}\]
Simplify \({3}^{4}\) to \(81\).
\[81{({a}^{2})}^{4}{(2{a}^{6})}^{2}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[81{a}^{8}{(2{a}^{6})}^{2}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[81{a}^{8}\times {2}^{2}{({a}^{6})}^{2}\]
Simplify \({2}^{2}\) to \(4\).
\[81{a}^{8}\times 4{({a}^{6})}^{2}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[81{a}^{8}\times 4{a}^{12}\]
Take out the constants.
\[(81\times 4){a}^{8}{a}^{12}\]
Simplify \(81\times 4\) to \(324\).
\[324{a}^{8}{a}^{12}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[324{a}^{8+12}\]
Simplify \(8+12\) to \(20\).
\[324{a}^{20}\]
324*a^20
