Product Rule

Reference > Algebra: Exponents

Description

The Product Rule states that:

\({x}^{a}{x}^{b}={x}^{a+b}\)
Examples

Example 1

\[{x}^{3}{x}^{2}{x}^{4}\]
1
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{3+2+4}\]

2
Simplify  \(3+2+4\)  to  \(9\).
\[{x}^{9}\]

Done


 

Example 2

\[{(x+3)}^{2}{(x+3)}^{3}\]
1
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{(x+3)}^{5}\]

Done


 

Example 3

\[\sin^{3}x\cos{x}\sin{x}\]
1
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\sin^{4}x\cos{x}\]

Done