Question

$$\frac{a^{3}\times a^{5}}{(a^{3})^{2}}$$

Answer

$$a^2$$

Solution


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