Question #79897

1 Answer
Oct 16, 2016

Answer:

#root(3)(7x)/root(3)(3y)=root(3)(63xy^2)/(3y)#

Explanation:

Assuming "rationalize" refers to rationalizing the denominator , note that #root(3)(3y)# is the value such that #(root(3)(3y))^3 = 3y#. We will use that fact to eliminate the root from the denominator.

#root(3)(7x)/root(3)(3y) = (root(3)(7x) * (root(3)(3y))^2) / (root(3)(3y) * (root(3)(3y))^2)#

#=(root(3)(7x) * root(3)((3y)^2))/(root(3)(3y))^3#

#=root(3)(7x*(3y)^2)/(3y)#

#=root(3)(63xy^2)/(3y)#

(Note that we also used the properties #(root(a)(x))^b = root(a)(x^b)# and #root(a)(x)*root(a)(y) = root(a)(xy)# during the process)