# How do you simplify  3a^2 * 3a?

#### Answer:

$3 {a}^{2} \cdot 3 a = \left(3 \cdot a \cdot a\right) \cdot \left(3 \cdot a\right) = 3 \cdot 3 \cdot a \cdot a \cdot a = 9 {a}^{3}$

#### Explanation:

We're being asked to simplify the expression $3 {a}^{2} \cdot 3 a$.

Looking at this problem as it is expressed, with two terms and different powers of a. Looking at it this way, it would appear that this expression is already simplified!

But let's look at it a different way and what the expressions are saying.

$3 {a}^{2}$ is saying that there's a 3 and it's multiplying the ${a}^{2}$.
${a}^{2}$ is saying that there are two a's multiplying each other. So,

$3 {a}^{2} = 3 \cdot a \cdot a$

$3 a$ works the same way - it's a 3 times an a, so

$3 a = 3 \cdot a$

So we can say:

$3 {a}^{2} \cdot 3 a = \left(3 \cdot a \cdot a\right) \cdot \left(3 \cdot a\right)$ - with the brackets there to help see the original.

We can now combine this expression into one expression - the 3's will multiply to get us 9, and the 3 a's multiply together to make ${a}^{3}$, so the final answer is:

$3 {a}^{2} \cdot 3 a = \left(3 \cdot a \cdot a\right) \cdot \left(3 \cdot a\right) = 3 \cdot 3 \cdot a \cdot a \cdot a = 9 {a}^{3}$