# How do you multiply 2x ^ { 2} y ^ { 5} ( 9x ^ { 3} y ) ^ { - 3}?

Aug 22, 2017

See below.

#### Explanation:

Let's deal with the value inside the parenthesis first.

$2 {x}^{2} {y}^{5} {\left(9 {x}^{3} y\right)}^{- 3}$

Remember that ${x}^{-} a = \frac{1}{x} ^ a$

${\left(9 {x}^{3} y\right)}^{- 3} = {9}^{-} 3 {x}^{-} 9 {y}^{-} 3 = \frac{1}{729 {x}^{9} {y}^{3}}$

Combining,

$2 {x}^{2} {y}^{5} {\left(9 {x}^{3} y\right)}^{- 3} = 2 {x}^{2} {y}^{5} \cdot \frac{1}{729 {x}^{9} {y}^{3}}$

${x}^{a} / {x}^{b} = {x}^{a - b}$

So,

$2 {x}^{2} {y}^{5} \cdot \frac{1}{729 {x}^{9} {y}^{3}} = \setminus \frac{2 {y}^{2}}{729 {x}^{7}}$

Since $2$ and $9$ have no common multiples, this is our solution.