How do you simplify #(((27 x^2 y) ^(1/2) (3xy)) ^(1/2)) / (5 x^(1/2) y^2)#?

1 Answer
Sep 6, 2017

Answer:

#color(magenta)((3^(5/4)x^(1/2))/(5y^(5/4))#

Explanation:

#(((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))#