Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{a}^{2x+5}{a}^{3(2x+1)}}{{({a}^{3})}^{2x+2}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{a}^{2x+5+3(2x+1)}}{{({a}^{3})}^{2x+2}}\]
Expand.
\[\frac{{a}^{2x+5+6x+3}}{{({a}^{3})}^{2x+2}}\]
Collect like terms.
\[\frac{{a}^{(2x+6x)+(5+3)}}{{({a}^{3})}^{2x+2}}\]
Simplify \((2x+6x)+(5+3)\) to \(8x+8\).
\[\frac{{a}^{8x+8}}{{({a}^{3})}^{2x+2}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{a}^{8x+8}}{{a}^{3(2x+2)}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{a}^{8x+8-3(2x+2)}\]
Expand.
\[{a}^{8x+8-6x-6}\]
Collect like terms.
\[{a}^{(8x-6x)+(8-6)}\]
Simplify \((8x-6x)+(8-6)\) to \(2x+2\).
\[{a}^{2x+2}\]
a^(2*x+2)
