# How do you simplify (-3a^2)(2a^3)^2?

Sep 23, 2015

The answer is $- 12 {a}^{8}$.

#### Explanation:

$\left(- 3 {a}^{2}\right) {\left(2 {a}^{3}\right)}^{2}$

Apply exponent rule ${\left({a}^{m}\right)}^{n} = \left({a}^{m \cdot n}\right)$.

Simplify ${\left(2 {a}^{3}\right)}^{2}$ to $\left(4 {a}^{6}\right)$ .

Because in $\left(- 3 {a}^{2}\right) {\left(2 {a}^{3}\right)}^{2}$ the square is being applied to both terms i.e ${\left(2\right)}^{2}$ and ${\left({a}^{3}\right)}^{2}$

Now,

$\left(- 3 {a}^{2}\right) \left(4 {a}^{6}\right)$

Apply exponent rule $\left({a}^{m} \cdot {a}^{n}\right) = {a}^{m + n}$.

Simplify.

$- 3 \times 4 \times {a}^{2 + 6} =$

$- 12 {a}^{8}$