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

2 Answers
Sep 19, 2016

#color(green)(x^(2/3)y^(3/2))#

Explanation:

#(x^(5/3)y)/(xy^(-1/2))#
#color(white)("XXX")=(x^(5/3))/(x) * (y)/(y^(-1/2))#

#color(white)("XXX")=(x^(5/3) * x^(-1)) * (y * y^(1/2))#

#color(white)("XXX")=x^(2/3) * y^(3/2)#

Sep 19, 2016

Just for comparison to Alan's

#color(maroon)(x^(2/3)y^(3/2))#

Explanation:

Given:#" "(x^(5/3)y)/(xy^(-1/2))#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write as: #" "(root(3)(x^3xx x^2)color(white)(..)ysqrt(y))/x #

#" "(cancel(x)^1root(3)(x^2)color(white)(..)ysqrt(y))/(cancel(x)^1 #

#root(3)(x^2) xx sqrt(y^2xxy)#

#x^(2/3)xxy^(3/2)#

#x^(2/3)y^(3/2)#