Question

$$\frac{(x^{2})^{3}(x^{2})^{5}}{x^{7}}$$

Answer

$$x^9$$

Solution


Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{6}{({x}^{2})}^{5}}{{x}^{7}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{6}{x}^{10}}{{x}^{7}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{x}^{6+10}}{{x}^{7}}\]
Simplify  \(6+10\)  to  \(16\).
\[\frac{{x}^{16}}{{x}^{7}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{x}^{16-7}\]
Simplify  \(16-7\)  to  \(9\).
\[{x}^{9}\]