How do you simplify #(x^3y^2)^(3/2)/(x^-1y^(-2/3))^(1/4)#?

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Answer 1 · 2017-11-01T10:55:19

#color(magenta)(x^(19/4)y^(19/6)#

#((x^3y^2)^(3/2))/(x^-1y^(-2/3))^(1/4)#

#:.=(x^(9/2)y^(6/2))/(x^(-1/4)y^(-2/12))#

#:.=(x^(9/2)y^3)/(x^(-1/4)y^(-2/12))#

#:.=(x^(9/2)y^3)/(x^(-1/4)y^(-1/6))#

#:.=x^(9/2+1/4)y^(3+1/6)#

#:.=x^(9/2+1/4)y^(19/6)#

#:.=x^((18+1)/4)y^(19/6)#

#:.color(magenta)(=x^(19/4)y^(19/6)#