# How do you divide \frac { 3x ^ { 12} } { 27x ^ { 9} }?

##### 1 Answer
Sep 13, 2017

${x}^{3} / 9$

#### Explanation:

We can treat this expression as:

$\frac{3}{27} \cdot {x}^{12} / {x}^{9}$

If we just focus on the $\frac{3}{27}$ we can simplify this since both $3$ and $27$ are divisible by $3$. So...

$\frac{3 \div i \mathrm{de} 3}{27 \div i \mathrm{de} 3} = \frac{1}{9}$

Next, looking at ${x}^{12} / {x}^{9}$, we can apply the quotient rule of exponents: ${a}^{m} / {a}^{n} = {a}^{m - n}$. In other words, we keep the $x$ and just subtract the exponents.

${x}^{12} / {x}^{9} = {x}^{12 - 9} = {x}^{3}$

Putting both parts together we get...

$\frac{1}{9} \cdot {x}^{3} = \frac{1 {x}^{3}}{9} = {x}^{3} / 9 \leftarrow$ Final Answer