Question

$$\frac{(x^{2})^{3}(x^{-3})}{x}$$

Answer

$$x^2$$

Solution


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