# How do you multiply and simplify (\frac { 2x ^ { 2} } { y ^ { 3} } ) ^ { 3} ( \frac { y ^ { 2} } { 4x } ) ^ { 2}?

Jul 3, 2017

${x}^{4} / \left(2 {y}^{5}\right)$

#### Explanation:

${\left(\setminus \frac{2 {x}^{2}}{{y}^{3}}\right)}^{3} {\left(\setminus \frac{{y}^{2}}{4 x}\right)}^{2}$

Let's manage each fraction individually for now.

${\left(\setminus \frac{2 {x}^{2}}{{y}^{3}}\right)}^{3} = \frac{8 {x}^{6}}{y} ^ 9$

${\left(\setminus \frac{{y}^{2}}{4 x}\right)}^{2} = {y}^{4} / \left(16 {x}^{2}\right)$

Now we multiply. Remember that ${x}^{a} / {x}^{b} = {x}^{a - b}$.

$\frac{8 {x}^{6}}{y} ^ 9 \setminus \cdot {y}^{4} / \left(16 {x}^{2}\right) = {x}^{4} / \left(2 {y}^{5}\right)$