#(((27x^2y)^(1/2)(3xy))^(1/2))/((5x^(1/2)y^2))#
#:.=(((3^(3*1/2)x^(2*1/2)y^(1/2))(3xy))^(1/2))/(5x^(1/2)y^2)#
#:.=(((3^(3/2)xy^(1/2))(3xy))^(1/2))/(5x^(1/2)y^2)#
#:.=((3^(5/2)x^2y^(1/2+2/2))^(1/2))/(5x^(1/2)y^2)#
#:.=((3^(5/2)x^2y^(3/2))^(1/2))/(5x^(1/2)y^2)#
#:.=((3^(5/2*1/2)x^(2*1/2)y^(3/2*1/2)))/(5x^(1/2)y^2)#
#:.=((3^(5/4)xy^(3/4)))/(5x^(1/2)y^2)#
#:.=((3^(5/4)x^(1-1/2)y^(3/4-8/4)))/5#
#:.=((3^(5/4)x^(1/2)y^(-5/4)))/5#
#:.=color(magenta)((3^(5/4)x^(1/2))/(5y^(5/4))#