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

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Answer 1 · 2015-07-22T01:45:18

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

$((16x^2y)/(81xy^2))/((24x^2y)/(54x^3y^3))$

$=color(red)(((16x^2y)/(81xy^2)))*color(blue)(((54x^3y^3)/(24x^2y)))$

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

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

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

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

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

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

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