# How do you simplify (((27 x^2 y) ^(1/2) (3xy)) ^(1/2)) / (5 x^(1/2) y^2)?

##### 1 Answer
Sep 6, 2017

color(magenta)((3^(5/4)x^(1/2))/(5y^(5/4))

#### Explanation:

$\frac{{\left({\left(27 {x}^{2} y\right)}^{\frac{1}{2}} \left(3 x y\right)\right)}^{\frac{1}{2}}}{\left(5 {x}^{\frac{1}{2}} {y}^{2}\right)}$

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

$\therefore = \frac{{\left(\left({3}^{\frac{3}{2}} x {y}^{\frac{1}{2}}\right) \left(3 x y\right)\right)}^{\frac{1}{2}}}{5 {x}^{\frac{1}{2}} {y}^{2}}$

$\therefore = \frac{{\left({3}^{\frac{5}{2}} {x}^{2} {y}^{\frac{1}{2} + \frac{2}{2}}\right)}^{\frac{1}{2}}}{5 {x}^{\frac{1}{2}} {y}^{2}}$

$\therefore = \frac{{\left({3}^{\frac{5}{2}} {x}^{2} {y}^{\frac{3}{2}}\right)}^{\frac{1}{2}}}{5 {x}^{\frac{1}{2}} {y}^{2}}$

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

$\therefore = \frac{\left({3}^{\frac{5}{4}} x {y}^{\frac{3}{4}}\right)}{5 {x}^{\frac{1}{2}} {y}^{2}}$

$\therefore = \frac{\left({3}^{\frac{5}{4}} {x}^{1 - \frac{1}{2}} {y}^{\frac{3}{4} - \frac{8}{4}}\right)}{5}$

$\therefore = \frac{\left({3}^{\frac{5}{4}} {x}^{\frac{1}{2}} {y}^{- \frac{5}{4}}\right)}{5}$

:.=color(magenta)((3^(5/4)x^(1/2))/(5y^(5/4))