How do you rationalize the denominator and simplify #1/root3(x^2)#?

2 Answers
Oct 17, 2017

Answer:

#1/root(3)(x^2)=color(red)(x^(-4/3))#

Explanation:

#1/root(3)(x^2)#
#color(white)("XXX")=1/root(3)(x^2)xxroot(3)(x^2)/root(3)(x^2)xxroot(3)(x^2)/root(3)(x^2)#

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

#color(white)("XXX")=(x^(1/3))^2xx`1/(x^2)#

#color(white)("XXX")=x^(2/3) xx x^(-2)#

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

#color(white)("XXX")=x^((-4/3))#

Oct 17, 2017

Answer:

See a solution process below:

Explanation:

To rationalize the denominator we must multiply the fraction by the appropriate value of #1#:

#root(3)(x)/root(3)(x) xx 1/root(3)(x^2) =>#

#(root(3)(x) xx 1)/(root(3)(x) xx root(3)(x^2)) =>#

#root(3)(x)/(root(3)(x xx x^2)) =>#

#root(3)(x)/(root(3)(x^3)) =>#

#root(3)(x)/x#