How do you simplify $\frac{\frac{16 x^{2} (y)}{81 x y^{2}}}{\frac{24 x^{2} (y)}{54 x^{3} (y^{3})}}$ $((16x^2(y))/(81xy^2))/((24x^2(y))/(54x^3(y^3)))$ ?

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How do you simplify $\frac{\frac{16 x^{2} (y)}{81 x y^{2}}}{\frac{24 x^{2} (y)}{54 x^{3} (y^{3})}}$ $((16x^2(y))/(81xy^2))/((24x^2(y))/(54x^3(y^3)))$ ?

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Answer 1 · 2015-07-22T01:45:18

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

Explanation:

$\frac{\frac{16 x^{2} y}{81 x y^{2}}}{\frac{24 x^{2} y}{54 x^{3} y^{3}}}$ $((16x^2y)/(81xy^2))/((24x^2y)/(54x^3y^3))$

$= (\frac{16 x^{2} y}{81 x y^{2}}) \cdot (\frac{54 x^{3} y^{3}}{24 x^{2} y})$ $=color(red)(((16x^2y)/(81xy^2)))*color(blue)(((54x^3y^3)/(24x^2y)))$

$= \frac{(8) (2) (x^{2} y) (6) (9) (x y^{2}) (x^{2} y)}{(9) (9) (x y^{2}) (4) (6) (x^{2} y)}$ $=(color(red)((8)(2)(x^2y))color(blue)((6)(9)(xy^2)(x^2y)))/(color(red)((9)(9)(xy^2))color(blue)((4)(6)(x^2y)))$

$=((8)(2)cancel((x^2y))(6)(9)(xy^2)(x^2y))/((9)(9)(xy^2)(4)(6)cancel((x^2y)))$

$=((8)(2)(6)(9)cancel((xy^2))(x^2y))/((9)(9)cancel((xy^2))(4)(6))$

$=((8)(2)cancel((6))cancel((9))(x^2y))/((9)cancel((9))(4)cancel((6)))$

$=(cancel((8))^2(2)(x^2y))/((9)cancel((4)))$

$=(4x^2y)/9$

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How do you simplify $\frac{\frac{16 x^{2} (y)}{81 x y^{2}}}{\frac{24 x^{2} (y)}{54 x^{3} (y^{3})}}$ $((16x^2(y))/(81xy^2))/((24x^2(y))/(54x^3(y^3)))$ ?

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How do you simplify $\frac{\frac{16 x^{2} (y)}{81 x y^{2}}}{\frac{24 x^{2} (y)}{54 x^{3} (y^{3})}}$ $((16x^2(y))/(81xy^2))/((24x^2(y))/(54x^3(y^3)))$ ?