How do you simplify  ((16x^2(y))/(81xy^2))/((24x^2(y))/(54x^3(y^3)))?

Jul 22, 2015

$\frac{\frac{16 {x}^{2} y}{81 x {y}^{2}}}{\frac{24 {x}^{2} y}{54 {x}^{3} {y}^{3}}} = \frac{4 {x}^{2} y}{9}$

Explanation:

$\frac{\frac{16 {x}^{2} y}{81 x {y}^{2}}}{\frac{24 {x}^{2} y}{54 {x}^{3} {y}^{3}}}$

$= \textcolor{red}{\left(\frac{16 {x}^{2} y}{81 x {y}^{2}}\right)} \cdot \textcolor{b l u e}{\left(\frac{54 {x}^{3} {y}^{3}}{24 {x}^{2} y}\right)}$

$= \frac{\textcolor{red}{\left(8\right) \left(2\right) \left({x}^{2} y\right)} \textcolor{b l u e}{\left(6\right) \left(9\right) \left(x {y}^{2}\right) \left({x}^{2} y\right)}}{\textcolor{red}{\left(9\right) \left(9\right) \left(x {y}^{2}\right)} \textcolor{b l u e}{\left(4\right) \left(6\right) \left({x}^{2} y\right)}}$

$= \frac{\left(8\right) \left(2\right) \cancel{\left({x}^{2} y\right)} \left(6\right) \left(9\right) \left(x {y}^{2}\right) \left({x}^{2} y\right)}{\left(9\right) \left(9\right) \left(x {y}^{2}\right) \left(4\right) \left(6\right) \cancel{\left({x}^{2} y\right)}}$

$= \frac{\left(8\right) \left(2\right) \left(6\right) \left(9\right) \cancel{\left(x {y}^{2}\right)} \left({x}^{2} y\right)}{\left(9\right) \left(9\right) \cancel{\left(x {y}^{2}\right)} \left(4\right) \left(6\right)}$

$= \frac{\left(8\right) \left(2\right) \cancel{\left(6\right)} \cancel{\left(9\right)} \left({x}^{2} y\right)}{\left(9\right) \cancel{\left(9\right)} \left(4\right) \cancel{\left(6\right)}}$

$= \frac{{\cancel{\left(8\right)}}^{2} \left(2\right) \left({x}^{2} y\right)}{\left(9\right) \cancel{\left(4\right)}}$

$= \frac{4 {x}^{2} y}{9}$