# How do you multiply 3r ^ { 3} \cdot 2r ^ { 2} \cdot 3r?

Apr 24, 2017

See the solution process below:

#### Explanation:

First, rewrite this expression as:

$\left(3 \cdot 2 \cdot 3\right) \left({r}^{3} \cdot {r}^{2} \cdot r\right) = 18 \left({r}^{3} \cdot {r}^{2} \cdot r\right)$

Now, we can use these two rules for exponents to complete the multiplication:

$a = {a}^{\textcolor{g r e e n}{1}}$ and ${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$18 \left({r}^{3} \cdot {r}^{2} \cdot r\right) = 18 \left({r}^{\textcolor{red}{3}} \cdot {r}^{\textcolor{b l u e}{2}} \cdot {r}^{\textcolor{g r e e n}{1}}\right) = 18 {r}^{\textcolor{red}{3} + \textcolor{b l u e}{2} + \textcolor{g r e e n}{1}} = 18 {r}^{6}$

Apr 24, 2017

$3 {r}^{3} \cdot 2 {r}^{2} \cdot 3 r = 18 {r}^{6}$

#### Explanation:

Multiply the constants normally and add the exponents.
Like this,

$\textcolor{red}{3 {r}^{3} \cdot 2 {r}^{2}} \cdot 3 r$

$\textcolor{red}{6 {r}^{5}} \cdot 3 r$

$\textcolor{g r e e n}{6 {r}^{5} \cdot 3 r}$

$\textcolor{g r e e n}{18 {r}^{6}}$