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#