How do you simplify #(x^{2}y\div y)^{2}\times (y^{3}\div x)^{2}#?

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Answer 1 · 2017-05-04T15:36:14

#x^2y^6#

Cancelling out in multiply or divide is the same changing to #xx 1#

Write as: #((x^2y)/y)^2xx(y^3/x)^2#

#" "(x^2xxy/y)^2xx(y^3/x)^2#

but #y/y=1 and 1xx x^2=x^2#

#" "(x^2)^2xxy^6/x^2#

#" "x^4/x^2 xxy^6#

#" "x^2y^6#

Answer 2 · 2017-05-04T16:00:42

#color(blue)(x^2y^6#

#(x^2y-:y)^2 xx (y^3-:x)^2#

#:.=((x^2y)/y)^2 xx (y^3/x)^2#

#:.=(cancel(x^4)^(color(red)x^color(red)2)cancel(y^2)^color(red)1)/cancel(y^2)^color(red)1 xx y^6/cancel(x^2)^color(red)1#

#:.color(blue)(=x^2y^6#