# How do you multiply (2a^{2} b^{3} ) ( 3a^{7} b^{5} )^{3}?

Oct 13, 2016

$54 {a}^{23} {b}^{18}$

#### Explanation:

$\left(2 {a}^{2} {b}^{3}\right) \textcolor{red}{{\left(3 {a}^{7} {b}^{5}\right)}^{3}} \text{ } \leftarrow$ bracket with a power first

=$\left(2 {a}^{2} {b}^{3}\right) \times \textcolor{red}{\left(27 {a}^{21} {b}^{15}\right)}$

Now multiply the numbers and the add the indices of like bases.

=$\textcolor{b l u e}{2 \times 27} \textcolor{\lim e}{{a}^{2} {a}^{21}} \textcolor{m a \ge n t a}{{b}^{3} {b}^{15}}$

$\textcolor{b l u e}{54} \textcolor{\lim e}{{a}^{23}} \textcolor{m a \ge n t a}{{b}^{18}}$