How do you simplify #(root3(-162x^6))#?

1 Answer
Oct 3, 2015

Answer:

#root(3)(-162x^6) = x^2(-3root(3)(6))#

Explanation:

We can take a minus out of the root, because #-1 = (-1)^3#

#-root(3)(162x^6)#

We know that #x^6 = x^2 * x^2 * x^2# or #x^6 = (x^2)^3#, so we can take a #x^2# out of the root

#-x^2root(3)(162)#

Lastly, all we have to do is factor the #162#, so

#162|2#
#color(white)(0)81|3#
#color(white)(0)27|3#
#color(white)(00)9|3#
#color(white)(00)3|3#
#color(white)(00)1|2*3^4#

So we can take a #3# out of the root, leaving a #2*3#, that is, #6# inside it. So

#root(3)(-162x^6) = x^2(-3root(3)(6))#