# How do you multiply (x ^ { 2} y ^ { 4} ) ^ { 3} \cdot 2x ^ { 3} y ^ { 5}?

##### 1 Answer
Jun 22, 2018

We will use two exponent rules to solve this one: ${\left({a}^{b}\right)}^{x} = {a}^{b \cdot x}$ and ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$.

#### Explanation:

Let's use the first rule to simplify the first half of the equation:

${\left({x}^{2} {y}^{4}\right)}^{3} = {x}^{2 \cdot 3} {y}^{4 \cdot 3} = {x}^{6} {y}^{12}$

We now have ${x}^{6} {y}^{12} \cdot 2 {x}^{3} {y}^{5}$. Let's now use the second rule:

$2 {x}^{6 + 3} {y}^{12 + 5} = 2 {x}^{9} {y}^{17}$